Meixner polynomials $M_n(x;\beta,c)$
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Polynomials
$\beta$
$c$
$n$ 
$M_n(x;\beta,c)$
1/2
1/4
0:
1
1/2
1/4
1:
-6*x + 1
1/2
1/4
2:
12*x^2 - 24*x + 1
1/2
1/4
3:
-72/5*x^3 + 396/5*x^2 - 414/5*x + 1
1/2
1/4
4:
432/35*x^4 - 4608/35*x^3 + 2664/7*x^2 - 9984/35*x + 1
1/2
1/4
5:
-288/35*x^5 + 144*x^4 - 5616/7*x^3 + 11496/7*x^2 - 35202/35*x + 1
1/2
1/4
6:
1728/385*x^6 - 44928/385*x^5 + 11664/11*x^4 - 45504/11*x^3 + 2609892/385*x^2 - 1396152/385*x + 1
1/2
1/4
7:
-10368/5005*x^7 + 53568/715*x^6 - 719712/715*x^5 + 908496/143*x^4 - 13997736/715*x^3 + 19604412/715*x^2 - 66580926/5005*x + 1
1/2
1/4
8:
20736/25025*x^8 - 995328/25025*x^7 + 2647296/3575*x^6 - 377856/55*x^5 + 121348512/3575*x^4 - 315277056/3575*x^3 + 2747625648/25025*x^2 - 247391808/5005*x + 1
1/2
1/4
9:
-124416/425425*x^9 + 7651584/425425*x^8 - 37698048/85085*x^7 + 31332096/5525*x^6 - 2487195072/60775*x^5 + 10267298208/60775*x^4 - 595974240/1547*x^3 + 186065548848/425425*x^2 - 15777587214/85085*x + 1
1/2
1/4
10:
746496/8083075*x^10 - 11446272/1616615*x^9 + 360370944/1616615*x^8 - 552904704/146965*x^7 + 43046308224/1154725*x^6 - 2714487552/12155*x^5 + 1296782480736/1616615*x^4 - 2665870966656/1616615*x^3 + 14042198768436/8083075*x^2 - 102995761272/146965*x + 1
1/2
1/4
11:
-1492992/56581525*x^11 + 746496/302575*x^10 - 5847552/60515*x^9 + 2138275584/1028755*x^8 - 19882361088/734825*x^7 + 162759466368/734825*x^6 - 1180353183552/1028755*x^5 + 3791558962656/1028755*x^4 - 35800024195512/5143775*x^3 + 35437304320692/5143775*x^2 - 4306969900362/1616615*x + 1
1/2
1/4
12:
8957952/1301375075*x^12 - 143327232/185910725*x^11 + 4349085696/118306825*x^10 - 1222262784/1245335*x^9 + 1920898250496/118306825*x^8 - 172954165248/994175*x^7 + 145000548050688/118306825*x^6 - 2725531711488/482885*x^5 + 1956016274841072/118306825*x^4 - 3439982640962304/118306825*x^3 + 35523417813284376/1301375075*x^2 - 29105674748352/2860165*x + 1
1/2
1/4
13:
-53747712/32534376875*x^13 + 546435072/2502644375*x^12 - 636014592/51074375*x^11 + 2626172928/6500375*x^10 - 1882910126592/227513125*x^9 + 25562415373056/227513125*x^8 - 234851426210304/227513125*x^7 + 58572269593344/9100525*x^6 - 45982293863328/1710625*x^5 + 2367681913778256/32501875*x^4 - 301711262641533648/2502644375*x^3 + 54109089232760664/500528875*x^2 - 1036383916064322/26558675*x + 1
1/2
1/4
14:
11943936/32534376875*x^14 - 23887872/422524375*x^13 + 38817792/10214875*x^12 - 52636925952/357520625*x^11 + 118881727488/32501875*x^10 - 1993718126592/32501875*x^9 + 32397076452096/45502625*x^8 - 187487133014016/32501875*x^7 + 150807213764928/4643125*x^6 - 4058418478817664/32501875*x^5 + 22634750513735568/71504125*x^4 - 16151749049017152/32501875*x^3 + 2785151335448077356/6506875375*x^2 - 27911470031392152/185910725*x + 1
1/2
1/4
15:
-71663616/943496929375*x^15 + 2544058368/188699385875*x^14 - 1236197376/1172045875*x^13 + 99728879616/2073619625*x^12 - 642146310144/450786875*x^11 + 5450795099136/188510875*x^10 - 545765230066176/1319576125*x^9 + 5570281592706816/1319576125*x^8 - 1706586230219904/55444375*x^7 + 1761980270841792/11088875*x^6 - 1179459208261096416/2073619625*x^5 + 97286416769957904/71504125*x^4 - 1923936954184699179624/943496929375*x^3 + 319784913081871732332/188699385875*x^2 - 183705428549842902/317141825*x + 1
1/2
1/4
16:
429981696/29248404810625*x^16 - 4586471424/1539389726875*x^15 + 1570006499328/5849680962125*x^14 - 11889280548864/835668708875*x^13 + 6921021210624/13974393125*x^12 - 3845760015532032/321411041875*x^11 + 8456890023862272/40906859875*x^10 - 106118844583477248/40906859875*x^9 + 4860356040604187136/204534299375*x^8 - 660994509745004544/4174169375*x^7 + 48747731957236237824/64282208375*x^6 - 163954925091570198528/64282208375*x^5 + 169541592422878072741824/29248404810625*x^4 - 494612033868307219968/59327393125*x^3 + 39251023607926261543392/5849680962125*x^2 - 374439919410550506624/167133741775*x + 1
1/2
1/3
0:
1
1/2
1/3
1:
-4*x + 1
1/2
1/3
2:
16/3*x^2 - 40/3*x + 1
1/2
1/3
3:
-64/15*x^3 + 144/5*x^2 - 548/15*x + 1
1/2
1/3
4:
256/105*x^4 - 3328/105*x^3 + 11552/105*x^2 - 2032/21*x + 1
1/2
1/3
5:
-1024/945*x^5 + 4352/189*x^4 - 29056/189*x^3 + 69856/189*x^2 - 81212/315*x + 1
1/2
1/3
6:
4096/10395*x^6 - 2048/165*x^5 + 280832/2079*x^4 - 430336/693*x^3 + 12175984/10395*x^2 - 2416552/3465*x + 1
1/2
1/3
7:
-16384/135135*x^7 + 20480/3861*x^6 - 1647616/19305*x^5 + 2457344/3861*x^4 - 43924288/19305*x^3 + 13923056/3861*x^2 - 86264956/45045*x + 1
1/2
1/3
8:
65536/2027025*x^8 - 3801088/2027025*x^7 + 12107776/289575*x^6 - 26599424/57915*x^5 + 766515712/289575*x^4 - 2278652416/289575*x^3 + 63144128/5775*x^2 - 239856352/45045*x + 1
1/2
1/3
9:
-262144/34459425*x^9 + 65536/116025*x^8 - 191430656/11486475*x^7 + 9224192/36465*x^6 - 3508197376/1640925*x^5 + 1855247872/182325*x^4 - 904062793472/34459425*x^3 + 8392195648/255255*x^2 - 11450125172/765765*x + 1
1/2
1/3
10:
1048576/654729075*x^10 - 19398656/130945815*x^9 + 243859456/43648605*x^8 - 4886757376/43648605*x^7 + 40629280768/31177575*x^6 - 2970423296/328185*x^5 + 4857495219712/130945815*x^4 - 11177149829632/130945815*x^3 + 650706424304/6613425*x^2 - 123134813896/2909907*x + 1
1/2
1/3
11:
-4194304/13749310575*x^11 + 42991616/1249937325*x^10 - 262144/162435*x^9 + 3438215168/83329155*x^8 - 37643190272/59520825*x^7 + 358775595008/59520825*x^6 - 8966712940544/249987465*x^5 + 32565397346816/249987465*x^4 - 113751328499008/416645775*x^3 + 40780578169424/138881925*x^2 - 26971805956/223839*x + 1
1/2
1/3
12:
16777216/316234143225*x^12 - 16777216/2342475135*x^11 + 11762925568/28748558475*x^10 - 24906825728/1916570565*x^9 + 2430383620096/9582852825*x^8 - 3408265216/1073709*x^7 + 742380768968704/28748558475*x^6 - 86551553368064/638856855*x^5 + 12796395772902656/28748558475*x^4 - 127169749388032/147428505*x^3 + 30739846185526112/35137127025*x^2 - 23079493413584/66927861*x + 1
1/2
1/3
13:
-67108864/7905853580625*x^13 + 16777216/12411073125*x^12 - 56178507776/608142583125*x^11 + 39449526272/11057137875*x^10 - 1591373201408/18428563125*x^9 + 1488478994432/1084033125*x^8 - 808638823333888/55285689375*x^7 + 33016894111744/315918225*x^6 - 27287594645808128/55285689375*x^5 + 82369331112506624/55285689375*x^4 - 547433994084257152/202714194375*x^3 + 35190353911235872/13514279625*x^2 - 1658062090208324/1673196525*x + 1
1/2
1/3
14:
268435456/213458046676875*x^14 - 7113539584/30494006668125*x^13 + 44073746432/2345692820625*x^12 - 406797156352/469138564125*x^11 + 95345967104/3741136875*x^10 - 5094502825984/10154514375*x^9 + 10111687679475712/1492713613125*x^8 - 2695155918700544/42648960375*x^7 + 86354098934460416/213244801875*x^6 - 372921682432206848/213244801875*x^5 + 3837701539936516864/781897606875*x^4 - 62521136043067648/7446643875*x^3 + 2449511943624618512/316234143225*x^2 - 2868700311292696/1003917915*x + 1
1/2
1/3
15:
-1073741824/6190283353629375*x^15 + 268435456/7240097489625*x^14 - 614784303104/176865238675125*x^13 + 856661426176/4535006119875*x^12 - 450766242316288/68025091798125*x^11 + 65210225262592/412273283625*x^10 - 22848766779588608/8657738956125*x^9 + 1302196278329344/41824825875*x^8 - 229454358720495616/883442750625*x^7 + 125035226842492928/82454656725*x^6 - 82468216484962229248/13605018359625*x^5 + 2496995764063841024/156379521375*x^4 - 17856341756807568117184/687809261514375*x^3 + 1056196261869427294064/45853950767625*x^2 - 63314949959275468/7661478825*x + 1
1/2
1/3
16:
4294967296/191898783962510625*x^16 - 1047972020224/191898783962510625*x^15 + 22628035198976/38379756792502125*x^14 - 204314815496192/5482822398928875*x^13 + 3242872979587072/2108777845741875*x^12 - 3181819348385792/72716477439375*x^11 + 12486093798637568/14125784612625*x^10 - 3451997718937862144/268389907639875*x^9 + 9561163178018996224/70628923063125*x^8 - 8551592397824589824/8335090299375*x^7 + 466071186753709703168/84351113829675*x^6 - 8706292420048914694144/421755569148375*x^5 + 173130240013519839828992/3366645332675625*x^4 - 1704260302530266482146304/21322087106945625*x^3 + 97349376723924485704064/1421472473796375*x^2 - 108124531476277008832/4512611027925*x + 1
1/2
1/2
0:
1
1/2
1/2
1:
-2*x + 1
1/2
1/2
2:
4/3*x^2 - 16/3*x + 1
1/2
1/2
3:
-8/15*x^3 + 28/5*x^2 - 166/15*x + 1
1/2
1/2
4:
16/105*x^4 - 64/21*x^3 + 1688/105*x^2 - 2224/105*x + 1
1/2
1/2
5:
-32/945*x^5 + 208/189*x^4 - 2096/189*x^3 + 1064/27*x^2 - 12406/315*x + 1
1/2
1/2
6:
64/10395*x^6 - 1024/3465*x^5 + 10064/2079*x^4 - 22784/693*x^3 + 132148/1485*x^2 - 35968/495*x + 1
1/2
1/2
7:
-128/135135*x^7 + 1216/19305*x^6 - 29408/19305*x^5 + 64880/3861*x^4 - 1675496/19305*x^3 + 3700804/19305*x^2 - 6047458/45045*x + 1
1/2
1/2
8:
256/2027025*x^8 - 2048/184275*x^7 + 107776/289575*x^6 - 70144/11583*x^5 + 1129504/22275*x^4 - 61676416/289575*x^3 + 271171216/675675*x^2 - 1248032/5005*x + 1
1/2
1/2
9:
-512/34459425*x^9 + 256/153153*x^8 - 77312/1044225*x^7 + 303872/182325*x^6 - 33725888/1640925*x^5 + 5089888/36465*x^4 - 17152371424/34459425*x^3 + 3159819248/3828825*x^2 - 356953546/765765*x + 1
1/2
1/2
10:
1024/654729075*x^10 - 4096/18706545*x^9 + 540928/43648605*x^8 - 16093184/43648605*x^7 + 195882112/31177575*x^6 - 20581888/328185*x^5 + 47189466976/130945815*x^4 - 21029583104/18706545*x^3 + 797651412/475475*x^2 - 12759816304/14549535*x + 1
1/2
1/2
11:
-2048/13749310575*x^11 + 31744/1249937325*x^10 - 49664/27776385*x^9 + 5660416/83329155*x^8 - 90966784/59520825*x^7 + 1252807552/59520825*x^6 - 44333497408/249987465*x^5 + 221987285152/249987465*x^4 - 1032093625256/416645775*x^3 + 470056014796/138881925*x^2 - 24147295174/14549535*x + 1
1/2
1/2
12:
4096/316234143225*x^12 - 16384/6200669475*x^11 + 382976/1691091675*x^10 - 45056/4212243*x^9 + 2942584576/9582852825*x^8 - 2544932864/456326325*x^7 + 143115319552/2211427575*x^6 - 2811657728/5933655*x^5 + 60738726147536/28748558475*x^4 - 7337373934144/1368978975*x^3 + 238736639473928/35137127025*x^2 - 150923708336/47805615*x + 1
1/2
1/2
13:
-8192/7905853580625*x^13 + 151552/608142583125*x^12 - 15536128/608142583125*x^11 + 16234496/11057137875*x^10 - 5993984/114463125*x^9 + 3191762176/2632651875*x^8 - 1024320817664/55285689375*x^7 + 412357881088/2211427575*x^6 - 67015208471584/55285689375*x^5 + 270517453843472/55285689375*x^4 - 331231359731408/28959170625*x^3 + 26244554481688/1930611375*x^2 - 10092814073242/1673196525*x + 1
1/2
1/2
14:
16384/213458046676875*x^14 - 131072/6098801333625*x^13 + 6090752/2345692820625*x^12 - 418512896/2345692820625*x^11 + 550083584/71081600625*x^10 - 3162054656/14216320125*x^9 + 340052616448/78563874375*x^8 - 12215165943808/213244801875*x^7 + 4735324948288/9271513125*x^6 - 127799663077888/42648960375*x^5 + 8675180273162224/781897606875*x^4 - 6294500908557824/260632535625*x^3 + 42906688953671524/1581170716125*x^2 - 58072723223072/5019589575*x + 1
1/2
1/2
15:
-32768/6190283353629375*x^15 + 704512/412685556908625*x^14 - 42459136/176865238675125*x^13 + 88133632/4535006119875*x^12 - 68523309056/68025091798125*x^11 + 763507712/21698593875*x^10 - 7353190938112/8657738956125*x^9 + 41256831077632/2885912985375*x^8 - 1034860756229504/6184099254375*x^7 + 553921623120448/412273283625*x^6 - 98057274239923232/13605018359625*x^5 + 3868327622249008/156379521375*x^4 - 1512329135373200776/29904750500625*x^3 + 2479974129944476468/45853950767625*x^2 - 3240598748835614/145568097675*x + 1
1/2
1/2
16:
65536/191898783962510625*x^16 - 1048576/8343425389674375*x^15 + 781058048/38379756792502125*x^14 - 10510139392/5482822398928875*x^13 + 35250159616/301253977963125*x^12 - 10294602039296/2108777845741875*x^11 + 7681714511872/53677981527975*x^10 - 801139884703744/268389907639875*x^9 + 2589629804713472/58345632095625*x^8 - 89535588768272384/191707076885625*x^7 + 206089176137640448/60250795592625*x^6 - 7150215410793565184/421755569148375*x^5 + 3479948427006380269888/63966261320836875*x^4 - 2243032830373397666048/21322087106945625*x^3 + 153061584257325343648/1421472473796375*x^2 - 11402837580711232/265447707525*x + 1
1/2
2/3
0:
1
1/2
2/3
1:
-x + 1
1/2
2/3
2:
1/3*x^2 - 7/3*x + 1
1/2
2/3
3:
-1/15*x^3 + 6/5*x^2 - 62/15*x + 1
1/2
2/3
4:
1/105*x^4 - 34/105*x^3 + 61/21*x^2 - 692/105*x + 1
1/2
2/3
5:
-1/945*x^5 + 11/189*x^4 - 187/189*x^3 + 1117/189*x^2 - 449/45*x + 1
1/2
2/3
6:
1/10395*x^6 - 3/385*x^5 + 446/2079*x^4 - 241/99*x^3 + 113464/10395*x^2 - 50893/3465*x + 1
1/2
2/3
7:
-1/135135*x^7 + 16/19305*x^6 - 59/1755*x^5 + 217/351*x^4 - 9257/1755*x^3 + 366319/19305*x^2 - 958834/45045*x + 1
1/2
2/3
8:
1/2027025*x^8 - 148/2027025*x^7 + 1186/289575*x^6 - 6428/57915*x^5 + 444517/289575*x^4 - 276836/26325*x^3 + 7134802/225225*x^2 - 1377952/45045*x + 1
1/2
2/3
9:
-1/34459425*x^9 + 1/182325*x^8 - 934/2297295*x^7 + 926/60775*x^6 - 509539/1640925*x^5 + 209553/60775*x^4 - 136316086/6891885*x^3 + 9373682/182325*x^2 - 33529061/765765*x + 1
1/2
2/3
10:
1/654729075*x^10 - 47/130945815*x^9 + 1483/43648605*x^8 - 73438/43648605*x^7 + 1478173/31177575*x^6 - 254519/328185*x^5 + 943781731/130945815*x^4 - 4668022186/130945815*x^3 + 5947747999/72747675*x^2 - 82783873/1322685*x + 1
1/2
2/3
11:
-1/13749310575*x^11 + 2/96149025*x^10 - 4/1633905*x^9 + 12899/83329155*x^8 - 343013/59520825*x^7 + 7755908/59520825*x^6 - 445741136/249987465*x^5 + 3568709423/249987465*x^4 - 1364233723/21928725*x^3 + 17789571584/138881925*x^2 - 1302130358/14549535*x + 1
1/2
2/3
12:
1/316234143225*x^12 - 2/1849322475*x^11 + 4453/28748558475*x^10 - 23336/1916570565*x^9 + 792238/1368978975*x^8 - 7886642/456326325*x^7 + 9394030609/28748558475*x^6 - 819717368/212952285*x^5 + 779708715386/28748558475*x^4 - 1014771066494/9582852825*x^3 + 996187202861/5019589575*x^2 - 3298715668/25741485*x + 1
1/2
2/3
13:
-1/7905853580625*x^13 + 31/608142583125*x^12 - 5309/608142583125*x^11 + 1319/1579591125*x^10 - 909122/18428563125*x^9 + 34654096/18428563125*x^8 - 2595237367/55285689375*x^7 + 1688732257/2211427575*x^6 - 437285610602/55285689375*x^5 + 393759206888/7897955625*x^4 - 35826764818843/202714194375*x^3 + 242395714499/794957625*x^2 - 307610445521/1673196525*x + 1
1/2
2/3
14:
1/213458046676875*x^14 - 67/30494006668125*x^13 + 208/469138564125*x^12 - 16991/335098974375*x^11 + 259061/71081600625*x^10 - 721892/4181270625*x^9 + 328358941/59708544525*x^8 - 25177084171/213244801875*x^7 + 15646841857/9271513125*x^6 - 475867885652/30463543125*x^5 + 13955284701599/156379521375*x^4 - 75675774065873/260632535625*x^3 + 38738376430822/83219511375*x^2 - 189551085437/717084225*x + 1
1/2
2/3
15:
-1/6190283353629375*x^15 + 4/45853950767625*x^14 - 3623/176865238675125*x^13 + 12517/4535006119875*x^12 - 16133482/68025091798125*x^11 + 34997/2560703625*x^10 - 4682787401/8657738956125*x^9 + 14248521664/961970995125*x^8 - 1727021885398/6184099254375*x^7 + 1469533487413/412273283625*x^6 - 406331208658141/13605018359625*x^5 + 151805637568/971301375*x^4 - 323928891202595221/687809261514375*x^3 + 32426776750750001/45853950767625*x^2 - 7921856130874/20795442525*x + 1
1/2
2/3
16:
1/191898783962510625*x^16 - 8/2492191999513125*x^15 + 3028/3489068799318375*x^14 - 746024/5482822398928875*x^13 + 29045662/2108777845741875*x^12 - 2000627152/2108777845741875*x^11 + 12255563192/268389907639875*x^10 - 8507445032/5477345053875*x^9 + 50106386838541/1341949538199375*x^8 - 120440570758288/191707076885625*x^7 + 3058713286746664/421755569148375*x^6 - 2131272411407768/38341415377125*x^5 + 1563192540357496618/5815114665530625*x^4 - 2302588690495105528/3046012443849375*x^3 + 1521384682223345756/1421472473796375*x^2 - 354717694893664/644658718275*x + 1
1/2
3/4
0:
1
1/2
3/4
1:
-2/3*x + 1
1/2
3/4
2:
4/27*x^2 - 40/27*x + 1
1/2
3/4
3:
-8/405*x^3 + 68/135*x^2 - 1006/405*x + 1
1/2
3/4
4:
16/8505*x^4 - 256/2835*x^3 + 9752/8505*x^2 - 704/189*x + 1
1/2
3/4
5:
-32/229635*x^5 + 496/45927*x^4 - 11888/45927*x^3 + 100328/45927*x^2 - 403366/76545*x + 1
1/2
3/4
6:
64/7577955*x^6 - 2432/2525985*x^5 + 56528/1515591*x^4 - 100288/168399*x^3 + 28507756/7577955*x^2 - 2599144/360855*x + 1
1/2
3/4
7:
-128/295540245*x^7 + 64/938223*x^6 - 164192/42220035*x^5 + 282736/2814669*x^4 - 50784296/42220035*x^3 + 17092772/2814669*x^2 - 316332974/32837805*x + 1
1/2
3/4
8:
256/13299311025*x^8 - 4096/1023023925*x^7 + 599296/1899901575*x^6 - 4557824/379980315*x^5 + 441729952/1899901575*x^4 - 4233953536/1899901575*x^3 + 1539529648/164189025*x^2 - 3754013632/295540245*x + 1
1/2
3/4
9:
-512/678264862275*x^9 + 15104/75362762475*x^8 - 4715008/226088287425*x^7 + 786688/717740595*x^6 - 1010445248/32298326775*x^5 + 44684384/92018025*x^4 - 2633924992096/678264862275*x^3 + 3842313392/274046409*x^2 - 250094855146/15072552495*x + 1
1/2
3/4
10:
1024/38661097149675*x^10 - 2048/234309679695*x^9 + 2992384/2577406476645*x^8 - 69244928/859135492215*x^7 + 5854076032/1841004626175*x^6 - 36119296/496897335*x^5 + 560033415136/594786109995*x^4 - 16664415572096/2577406476645*x^3 + 87928640325556/4295677461075*x^2 - 112167535528/5206881771*x + 1
1/2
3/4
11:
-2048/2435649120429525*x^11 + 74752/221422647311775*x^10 - 822784/14761509820785*x^9 + 72914176/14761509820785*x^8 - 142848256/554943978225*x^7 + 85758952576/10543935586275*x^6 - 6871119055168/44284529462355*x^5 + 76427677638112/44284529462355*x^4 - 255729181455032/24602516367975*x^3 + 55528748297956/1892501259075*x^2 - 4786916610482/171827098443*x + 1
1/2
3/4
12:
4096/168059789309637225*x^12 - 131072/11203985953975815*x^11 + 35903488/15278162664512475*x^10 - 9764864/37723858430895*x^9 + 87694456576/5092720888170825*x^8 - 34856648704/48502103696865*x^7 + 22269147420928/1175243281885575*x^6 - 316115551649792/1018544177634165*x^5 + 46252157532253136/15278162664512475*x^4 - 5519023972725248/339514725878055*x^3 + 59559871799657384/1436408455637925*x^2 - 32781156836096/912005368659*x + 1
1/2
3/4
13:
-8192/12604484198222791875*x^13 + 118784/323191902518533125*x^12 - 5033984/57033865150329375*x^11 + 858112/72545881597875*x^10 - 28735399424/29381082047139375*x^9 + 72896449792/1399099145101875*x^8 - 159923592548864/88143246141418125*x^7 + 48264992745728/1175243281885575*x^6 - 51982249379927584/88143246141418125*x^5 + 2953517552632624/576099647983125*x^4 - 157563466301957456/6337096127814375*x^3 + 19815720653310632/342002013247125*x^2 - 1525469931792362/32933527201575*x + 1
1/2
3/4
14:
16384/1020963220056046141875*x^14 - 1540096/145851888579435163125*x^13 + 4788224/1602768006367419375*x^12 - 1073987584/2243875208914387125*x^11 + 16369163264/339981092259755625*x^10 - 1083820828672/339981092259755625*x^9 + 1011605285586688/7139602937454868125*x^8 - 863934483666944/203988655355853375*x^7 + 12243712718848832/145706182397038125*x^6 - 1096493220220579712/1019943276779266875*x^5 + 31549649455974234736/3739792014857311875*x^4 - 9311234698037391808/249319467657154125*x^3 + 121363530548606449172/1512538103786735025*x^2 - 286499427772773256/4801708265989635*x + 1
1/2
3/4
15:
-32768/88823800144876014343125*x^15 + 1654784/5921586676325067622875*x^14 - 233463808/2537822861282171838375*x^13 + 34238464/1971890335106582625*x^12 - 88611899392/42438509385989495625*x^11 + 994939864064/5915671005319747875*x^10 - 1154087036694016/124229091111714705375*x^9 + 863223217098496/2435864531602249125*x^8 - 117680830481309312/12676437868542316875*x^7 + 21566105130241216/131459355673772175*x^6 - 369692521727689352096/195217143175551679875*x^5 + 30416169827125030288/2243875208914387125*x^4 - 545389390965696481607288/9869311127208446038125*x^3 + 6598405694818359643268/59814006831566339625*x^2 - 160563378725586513494/2088743095705491225*x + 1
1/2
3/4
16:
65536/8260613413473469333910625*x^16 - 2097152/305948644943461827181875*x^15 + 4291690496/1652122682694693866782125*x^14 - 6411517952/11238929814249618141375*x^13 + 7336156413952/90775971576631531141875*x^12 - 235459232792576/30258657192210510380625*x^11 + 6040785014546432/11553305473389467599875*x^10 - 31816214584918016/1283700608154385288875*x^9 + 47857531242348100096/57766527366947337999375*x^8 - 53159660042014449664/2750787017473682761875*x^7 + 58866913374638807552/191107308582382170825*x^6 - 19617554798630437480448/6051731438442102076125*x^5 + 2177208045989602367464384/101982881647820609060625*x^4 - 24705062364122063566089728/305948644943461827181875*x^3 + 3075347725639759833633248/20396576329564121812125*x^2 - 377429549509854399872/3808884468639425175*x + 1
1
1/4
0:
1
1
1/4
1:
-3*x + 1
1
1/4
2:
9/2*x^2 - 21/2*x + 1
1
1/4
3:
-9/2*x^3 + 27*x^2 - 63/2*x + 1
1
1/4
4:
27/8*x^4 - 153/4*x^3 + 945/8*x^2 - 381/4*x + 1
1
1/4
5:
-81/40*x^5 + 297/8*x^4 - 1737/8*x^3 + 3735/8*x^2 - 5997/20*x + 1
1
1/4
6:
81/80*x^6 - 2187/80*x^5 + 4131/16*x^4 - 16749/16*x^3 + 17793/10*x^2 - 19647/20*x + 1
1
1/4
7:
-243/560*x^7 + 81/5*x^6 - 8991/40*x^5 + 5859/4*x^4 - 372321/80*x^3 + 134001/20*x^2 - 465189/140*x + 1
1
1/4
8:
729/4480*x^8 - 8991/1120*x^7 + 49167/320*x^6 - 117207/80*x^5 + 4757103/640*x^4 - 3166677/160*x^3 + 28188963/1120*x^2 - 3224103/280*x + 1
1
1/4
9:
-243/4480*x^9 + 2187/640*x^8 - 38637/448*x^7 + 361827/320*x^6 - 5345757/640*x^5 + 22560363/640*x^4 - 4592241/56*x^3 + 15147729/160*x^2 - 11379663/280*x + 1
1
1/4
10:
729/44800*x^10 - 11421/8960*x^9 + 6561/160*x^8 - 633501/896*x^7 + 45785331/6400*x^6 - 55966059/1280*x^5 + 716778477/4480*x^4 - 149798457/448*x^3 + 285665859/800*x^2 - 40739763/280*x + 1
1
1/4
11:
-2187/492800*x^11 + 9477/22400*x^10 - 21627/1280*x^9 + 1659933/4480*x^8 - 220215591/44800*x^7 + 131140053/3200*x^6 - 387035091/1792*x^5 + 3157523127/4480*x^4 - 2159130789/1600*x^3 + 7565479713/5600*x^2 - 1622542233/3080*x + 1
1
1/4
12:
2187/1971200*x^12 - 124659/985600*x^11 + 1100061/179200*x^10 - 2989143/17920*x^9 + 503125911/179200*x^8 - 2741042187/89600*x^7 + 39246517143/179200*x^6 - 3669247269/3584*x^5 + 136183117293/44800*x^4 - 121165640811/22400*x^3 + 78955252227/15400*x^2 - 5928694083/3080*x + 1
1
1/4
13:
-6561/25625600*x^13 + 67797/1971200*x^12 - 3930039/1971200*x^11 + 11779911/179200*x^10 - 245186271/179200*x^9 + 3380758641/179200*x^8 - 31528100367/179200*x^7 + 199378474893/179200*x^6 - 421832043891/89600*x^5 + 578350222983/44800*x^4 - 5317823253753/246400*x^3 + 37563052644/1925*x^2 - 283768321119/40040*x + 1
1
1/4
14:
19683/358758400*x^14 - 439587/51251200*x^13 + 461457/788480*x^12 - 12962349/563200*x^11 + 207975681/358400*x^10 - 505514601/51200*x^9 + 58310364807/501760*x^8 - 341988808779/358400*x^7 + 60933717477/11200*x^6 - 135413238699/6400*x^5 + 2670660416547/49280*x^4 - 3021365310399/35200*x^3 + 208715567659749/2802800*x^2 - 150213388917/5720*x + 1
1
1/4
15:
-19683/1793792000*x^15 + 177147/89689600*x^14 - 1003833/6406400*x^13 + 1428111/197120*x^12 - 2144220093/9856000*x^11 + 401045499/89600*x^10 - 20342622771/313600*x^9 + 84104765721/125440*x^8 - 8866565019999/1792000*x^7 + 1157170341843/44800*x^6 - 46033314596361/492800*x^5 + 1389002084523/6160*x^4 - 38185611738708087/112112000*x^3 + 798458528344599/2802800*x^2 - 559666937421/5720*x + 1
1
1/4
16:
59049/28700672000*x^16 - 19683/46592000*x^15 + 55328913/1435033600*x^14 - 53058807/25625600*x^13 + 11513389329/157696000*x^12 - 5030272773/2816000*x^11 + 313574495589/10035200*x^10 - 71108873487/179200*x^9 + 737928537689079/200704000*x^8 - 88765342488423/3584000*x^7 + 944629335430551/7884800*x^6 - 5205005270811/12800*x^5 + 1671279371669672361/1793792000*x^4 - 6174843379402851/4576000*x^3 + 24491312246306727/22422400*x^2 - 4190235490767/11440*x + 1
1
1/3
0:
1
1
1/3
1:
-2*x + 1
1
1/3
2:
2*x^2 - 6*x + 1
1
1/3
3:
-4/3*x^3 + 10*x^2 - 44/3*x + 1
1
1/3
4:
2/3*x^4 - 28/3*x^3 + 106/3*x^2 - 104/3*x + 1
1
1/3
5:
-4/15*x^5 + 6*x^4 - 128/3*x^3 + 110*x^2 - 1246/15*x + 1
1
1/3
6:
4/45*x^6 - 44/15*x^5 + 302/9*x^4 - 488/3*x^3 + 14596/45*x^2 - 1022/5*x + 1
1
1/3
7:
-8/315*x^7 + 52/45*x^6 - 872/45*x^5 + 1358/9*x^4 - 25376/45*x^3 + 42028/45*x^2 - 18084/35*x + 1
1
1/3
8:
2/315*x^8 - 8/21*x^7 + 44/5*x^6 - 1504/15*x^5 + 8998/15*x^4 - 5552/3*x^3 + 838948/315*x^2 - 46784/35*x + 1
1
1/3
9:
-4/2835*x^9 + 34/315*x^8 - 3104/945*x^7 + 772/15*x^6 - 60652/135*x^5 + 11042/5*x^4 - 16652408/2835*x^3 + 2385188/315*x^2 - 1109926/315*x + 1
1
1/3
10:
4/14175*x^10 - 76/2835*x^9 + 982/945*x^8 - 4048/189*x^7 + 173152/675*x^6 - 247492/135*x^5 + 21903814/2835*x^4 - 10348264/567*x^3 + 33910106/1575*x^2 - 2969938/315*x + 1
1
1/3
11:
-8/155925*x^11 + 4/675*x^10 - 808/2835*x^9 + 2354/315*x^8 - 555248/4725*x^7 + 258544/225*x^6 - 3976136/567*x^5 + 3522574/135*x^4 - 792681028/14175*x^3 + 96566866/1575*x^2 - 88470308/3465*x + 1
1
1/3
12:
4/467775*x^12 - 184/155925*x^11 + 2932/42525*x^10 - 6352/2835*x^9 + 90622/2025*x^8 - 300976/525*x^7 + 202946176/42525*x^6 - 72588896/2835*x^5 + 3653848724/42525*x^4 - 2405961004/14175*x^3 + 1299140474/7425*x^2 - 241923608/3465*x + 1
1
1/3
13:
-8/6081075*x^13 + 4/18711*x^12 - 6976/467775*x^11 + 25012/42525*x^10 - 206116/14175*x^9 + 95654/405*x^8 - 109274288/42525*x^7 + 797145856/42525*x^6 - 3840382216/42525*x^5 + 2361974836/8505*x^4 - 79805784152/155925*x^3 + 3715840154/7425*x^2 - 8669332634/45045*x + 1
1
1/3
14:
8/42567525*x^14 - 8/225225*x^13 + 124/42525*x^12 - 3056/22275*x^11 + 174856/42525*x^10 - 167156/2025*x^9 + 338321834/297675*x^8 - 51071792/4725*x^7 + 3001042424/42525*x^6 - 628215992/2025*x^5 + 414035017804/467775*x^4 - 34220556896/22275*x^3 + 616860340888/429975*x^2 - 24058532174/45045*x + 1
1
1/3
15:
-16/638512875*x^15 + 232/42567525*x^14 - 9488/18243225*x^13 + 2692/93555*x^12 - 7211872/7016625*x^11 + 354152/14175*x^10 - 379089896/893025*x^9 + 303554018/59535*x^8 - 27612394048/637875*x^7 + 10930957592/42525*x^6 - 1465106683696/1403325*x^5 + 87027100148/31185*x^4 - 326069758602176/70945875*x^3 + 433200204464/105105*x^2 - 67148296892/45045*x + 1
1
1/3
16:
2/638512875*x^16 - 496/638512875*x^15 + 10888/127702575*x^14 - 9088/1658475*x^13 + 1613684/7016625*x^12 - 46700992/7016625*x^11 + 122121688/893025*x^10 - 1807118336/893025*x^9 + 96685369442/4465125*x^8 - 106376476768/637875*x^7 + 1279855187528/1403325*x^6 - 4850814438016/1403325*x^5 + 206323673827724/23648625*x^4 - 88468262691136/6449625*x^3 + 3741207645256/315315*x^2 - 188338265792/45045*x + 1
1
1/2
0:
1
1
1/2
1:
-x + 1
1
1/2
2:
1/2*x^2 - 5/2*x + 1
1
1/2
3:
-1/6*x^3 + 2*x^2 - 29/6*x + 1
1
1/2
4:
1/24*x^4 - 11/12*x^3 + 131/24*x^2 - 103/12*x + 1
1
1/2
5:
-1/120*x^5 + 7/24*x^4 - 77/24*x^3 + 305/24*x^2 - 887/60*x + 1
1
1/2
6:
1/720*x^6 - 17/240*x^5 + 179/144*x^4 - 439/48*x^3 + 2453/90*x^2 - 1517/60*x + 1
1
1/2
7:
-1/5040*x^7 + 1/72*x^6 - 16/45*x^5 + 301/72*x^4 - 16717/720*x^3 + 2009/36*x^2 - 18239/420*x + 1
1
1/2
8:
1/40320*x^8 - 23/10080*x^7 + 77/960*x^6 - 991/720*x^5 + 7823/640*x^4 - 78941/1440*x^3 + 1120859/10080*x^2 - 63253/840*x + 1
1
1/2
9:
-1/362880*x^9 + 13/40320*x^8 - 901/60480*x^7 + 337/960*x^6 - 78613/17280*x^5 + 62617/1920*x^4 - 5595463/45360*x^3 + 2197799/10080*x^2 - 332839/2520*x + 1
1
1/2
10:
1/3628800*x^10 - 29/725760*x^9 + 71/30240*x^8 - 1759/24192*x^7 + 223513/172800*x^6 - 467321/34560*x^5 + 29629133/362880*x^4 - 9744281/36288*x^3 + 7115711/16800*x^2 - 118127/504*x + 1
1
1/2
11:
-1/39916800*x^11 + 1/226800*x^10 - 233/725760*x^9 + 1529/120960*x^8 - 357331/1209600*x^7 + 183007/43200*x^6 - 27040847/725760*x^5 + 70841243/362880*x^4 - 517989179/907200*x^3 + 4583777/5600*x^2 - 2331085/5544*x + 1
1
1/2
12:
1/479001600*x^12 - 1/2280960*x^11 + 241/6220800*x^10 - 2743/1451520*x^9 + 814711/14515200*x^8 - 102257/96768*x^7 + 554609221/43545600*x^6 - 20123071/207360*x^5 + 701413217/1555200*x^4 - 433161647/362880*x^3 + 656005981/415800*x^2 - 4222975/5544*x + 1
1
1/2
13:
-1/6227020800*x^13 + 19/479001600*x^12 - 2003/479001600*x^11 + 10777/43545600*x^10 - 132137/14515200*x^9 + 3159949/14515200*x^8 - 149881099/43545600*x^7 + 1563006211/43545600*x^6 - 5271423541/21772800*x^5 + 11050398281/10886400*x^4 - 49190304017/19958400*x^3 + 157890902/51975*x^2 - 100309579/72072*x + 1
1
1/2
14:
1/87178291200*x^14 - 41/12454041600*x^13 + 391/958003200*x^12 - 3943/136857600*x^11 + 111947/87091200*x^10 - 157801/4147200*x^9 + 465527521/609638400*x^8 - 908834753/87091200*x^7 + 261800249/2721600*x^6 - 908274257/1555200*x^5 + 134038850261/59875200*x^4 - 14375725631/2851200*x^3 + 442619349167/75675600*x^2 - 184649263/72072*x + 1
1
1/2
15:
-1/1307674368000*x^15 + 1/3962649600*x^14 - 97/2668723200*x^13 + 289/95800320*x^12 - 576523/3592512000*x^11 + 250801/43545600*x^10 - 130759453/914457600*x^9 + 151089511/60963840*x^8 - 39064160803/1306368000*x^7 + 269643461/1088640*x^6 - 492714908027/359251200*x^5 + 661181737/136080*x^4 - 93017156834471/9081072000*x^3 + 852641163173/75675600*x^2 - 1710440723/360360*x + 1
1
1/2
16:
1/20922789888000*x^16 - 47/2615348736000*x^15 + 283/95103590400*x^14 - 5359/18681062400*x^13 + 2062121/114960384000*x^12 - 11026507/14370048000*x^11 + 168884957/7315660800*x^10 - 452338993/914457600*x^9 + 1106479367071/146313216000*x^8 - 213943488911/2612736000*x^7 + 3549173659967/5748019200*x^6 - 2264508119239/718502400*x^5 + 412579637892833/39626496000*x^4 - 375938196240547/18162144000*x^3 + 13151052791389/605404800*x^2 - 6372905521/720720*x + 1
1
2/3
0:
1
1
2/3
1:
-1/2*x + 1
1
2/3
2:
1/8*x^2 - 9/8*x + 1
1
2/3
3:
-1/48*x^3 + 7/16*x^2 - 23/12*x + 1
1
2/3
4:
1/384*x^4 - 19/192*x^3 + 395/384*x^2 - 563/192*x + 1
1
2/3
5:
-1/3840*x^5 + 1/64*x^4 - 227/768*x^3 + 65/32*x^2 - 4081/960*x + 1
1
2/3
6:
1/46080*x^6 - 29/15360*x^5 + 521/9216*x^4 - 2183/3072*x^3 + 83837/23040*x^2 - 3829/640*x + 1
1
2/3
7:
-1/645120*x^7 + 17/92160*x^6 - 739/92160*x^5 + 2947/18432*x^4 - 69311/46080*x^3 + 70651/11520*x^2 - 18549/2240*x + 1
1
2/3
8:
1/10321920*x^8 - 13/860160*x^7 + 221/245760*x^6 - 1601/61440*x^5 + 63823/163840*x^4 - 359911/122880*x^3 + 25608707/2580480*x^2 - 814243/71680*x + 1
1
2/3
9:
-1/185794560*x^9 + 11/10321920*x^8 - 515/6193152*x^7 + 811/245760*x^6 - 634813/8847360*x^5 + 140653/163840*x^4 - 49979245/9289728*x^3 + 40281037/2580480*x^2 - 10012127/645120*x + 1
1
2/3
10:
1/3715891200*x^10 - 7/106168320*x^9 + 809/123863040*x^8 - 8423/24772608*x^7 + 1792213/176947200*x^6 - 6241357/35389440*x^5 + 163549397/92897280*x^4 - 50268169/5308416*x^3 + 620911079/25804800*x^2 - 6833851/322560*x + 1
1
2/3
11:
-1/81749606400*x^11 + 1/275251200*x^10 - 331/743178240*x^9 + 2431/82575360*x^8 - 2850481/2477260800*x^7 + 1079639/39321600*x^6 - 29655583/74317824*x^5 + 15694173/4587520*x^4 - 1874178419/116121600*x^3 + 58948219/1612800*x^2 - 205500907/7096320*x + 1
1
2/3
12:
1/1961990553600*x^12 - 59/326998425600*x^11 + 4783/178362777600*x^10 - 13043/5945425920*x^9 + 924793/8493465600*x^8 - 1251227/367001600*x^7 + 12112502029/178362777600*x^6 - 1008058529/1189085184*x^5 + 284344236389/44590694400*x^4 - 199426952411/7431782400*x^3 + 53456835373/973209600*x^2 - 2253090731/56770560*x + 1
1
2/3
13:
-1/51011754393600*x^13 + 1/122624409600*x^12 - 5669/3923981107200*x^11 + 12779/89181388800*x^10 - 1046687/118908518400*x^9 + 743197/2123366400*x^8 - 3263540557/356725555200*x^7 + 13959291827/89181388800*x^6 - 76443066289/44590694400*x^5 + 128213455331/11147673600*x^4 - 3576937610173/81749606400*x^3 + 79707337723/973209600*x^2 - 40282067333/738017280*x + 1
1
2/3
14:
1/1428329123020800*x^14 - 23/68015672524800*x^13 + 221/3139184885760*x^12 - 6221/747424972800*x^11 + 884537/1426902220800*x^10 - 2072929/67947724800*x^9 + 2022831011/1997663109120*x^8 - 10812517691/475634073600*x^7 + 243418541549/713451110400*x^6 - 56602090667/16986931200*x^5 + 7927177559027/392398110720*x^4 - 820388130949/11678515200*x^3 + 150545588719157/1239869030400*x^2 - 111237109141/1476034560*x + 1
1
2/3
15:
-1/42849873690624000*x^15 + 37/2856658246041600*x^14 - 3833/1224282105446400*x^13 + 2731/6278369771520*x^12 - 18183667/470877732864000*x^11 + 2191793/951268147200*x^10 - 5672264771/59929893273600*x^9 + 10779334541/3995326218240*x^8 - 1137033045389/21403533312000*x^7 + 507103358189/713451110400*x^6 - 73814417455967/11771943321600*x^5 + 283868786867/8174960640*x^4 - 517885400501639/4649508864000*x^3 + 12347669134399/68881612800*x^2 - 77114237279/738017280*x + 1
1
2/3
16:
1/1371195958099968000*x^16 - 79/171399494762496000*x^15 + 8777/68559797904998400*x^14 - 25283/1224282105446400*x^13 + 1475611/684913065984000*x^12 - 144294659/941755465728000*x^11 + 3658219421/479439146188800*x^10 - 16130620421/59929893273600*x^9 + 64515010285471/9588782923776000*x^8 - 20217324229087/171228266496000*x^7 + 537350966934959/376702186291200*x^6 - 540918124968443/47087773286400*x^5 + 186085722420378707/3174064717824000*x^4 - 208103019173319659/1190274269184000*x^3 + 317238480198293/1202297241600*x^2 - 6871398664181/47233105920*x + 1
1
3/4
0:
1
1
3/4
1:
-1/3*x + 1
1
3/4
2:
1/18*x^2 - 13/18*x + 1
1
3/4
3:
-1/162*x^3 + 5/27*x^2 - 191/162*x + 1
1
3/4
4:
1/1944*x^4 - 1/36*x^3 + 803/1944*x^2 - 557/324*x + 1
1
3/4
5:
-1/29160*x^5 + 17/5832*x^4 - 457/5832*x^3 + 4495/5832*x^2 - 11479/4860*x + 1
1
3/4
6:
1/524880*x^6 - 41/174960*x^5 + 1043/104976*x^4 - 2069/11664*x^3 + 85253/65610*x^2 - 136981/43740*x + 1
1
3/4
7:
-1/11022480*x^7 + 1/65610*x^6 - 737/787320*x^5 + 77/2916*x^4 - 554947/1574640*x^3 + 269353/131220*x^2 - 414269/102060*x + 1
1
3/4
8:
1/264539520*x^8 - 11/13226976*x^7 + 1319/18895680*x^6 - 13487/4723920*x^5 + 2279047/37791360*x^4 - 1213433/1889568*x^3 + 22784579/7348320*x^2 - 9520967/1837080*x + 1
1
3/4
9:
-1/7142567040*x^9 + 31/793618560*x^8 - 5113/1190427840*x^7 + 1513/6298560*x^6 - 2504293/340122240*x^5 + 4696259/37791360*x^4 - 491237897/446410440*x^3 + 899693453/198404640*x^2 - 324955189/49601160*x + 1
1
3/4
10:
1/214277011200*x^10 - 23/14285134080*x^9 + 401/1785641760*x^8 - 7837/476171136*x^7 + 7041913/10203667200*x^6 - 11506091/680244480*x^5 + 5093430533/21427701120*x^4 - 1286707403/714256704*x^3 + 19266488933/2976069600*x^2 - 408075457/49601160*x + 1
1
3/4
11:
-1/7071141369600*x^11 + 19/321415516800*x^10 - 437/42855402240*x^9 + 20317/21427701120*x^8 - 11167031/214277011200*x^7 + 26754937/15305500800*x^6 - 917849761/25713241344*x^5 + 27628226989/64283103360*x^4 - 16948073827/5952139200*x^3 + 81011104339/8928208800*x^2 - 1871211329/181870920*x + 1
1
3/4
12:
1/254561089305600*x^12 - 83/42426848217600*x^11 + 9463/23141917209600*x^10 - 4031/85710804480*x^9 + 25303351/7713972403200*x^8 - 185459833/1285662067200*x^7 + 93322649509/23141917209600*x^6 - 54451950937/771397240320*x^5 + 4302411315239/5785479302400*x^4 - 1407090891929/321415516800*x^3 + 2770330250329/220973167800*x^2 - 63031952633/4910514840*x + 1
1
3/4
13:
-1/9927882482918400*x^13 + 1/16970739287040*x^12 - 1601/109097609702400*x^11 + 47333/23141917209600*x^10 - 583411/3305988172800*x^9 + 3039049/308558896128*x^8 - 25066373791/69425751628800*x^7 + 66759510493/7713972403200*x^6 - 657572129293/4958982259200*x^5 + 1437351178913/1157095860480*x^4 - 9974591061823/1515244579200*x^3 + 473121723373/27621645975*x^2 - 1021200170509/63836692920*x + 1
1
3/4
14:
1/416971064282572800*x^14 - 97/59567294897510400*x^13 + 2183/4582099607500800*x^12 - 51791/654585658214400*x^11 + 1148729/138851503257600*x^10 - 11330977/19835929036800*x^9 + 77500291873/2915881568409600*x^8 - 348043359961/416554509772800*x^7 + 57060516031/3254332107600*x^6 - 1777476690049/7438473388800*x^5 + 192466398116431/95460408489600*x^4 - 44187670305149/4545733737600*x^3 + 2798448726144949/120651349618800*x^2 - 3817646624347/191510078760*x + 1
1
3/4
15:
-1/18763697892715776000*x^15 + 1/24056022939379200*x^14 - 43/3046054852713600*x^13 + 631/229104980375040*x^12 - 35379371/103097241168768000*x^11 + 8971729/312415882329600*x^10 - 2711443391/1640183382230400*x^9 + 28851894227/437382235261440*x^8 - 34033823814253/18744952939776000*x^7 + 1764823017113/52069313721600*x^6 - 2145011614988507/5154862058438400*x^5 + 17158106049487/5369647977540*x^4 - 167511279707072711/11845768871664000*x^3 + 520981785240479/16705571485680*x^2 - 42842438098459/1723590708840*x + 1
1
3/4
16:
1/900657498850357248000*x^16 - 37/37527395785431552000*x^15 + 17321/45032874942517862400*x^14 - 7783/89350942346265600*x^13 + 63098921/4948667576100864000*x^12 - 262175737/206194482337536000*x^11 + 27937008221/314915209388236800*x^10 - 57469113323/13121467057843200*x^9 + 963787351597471/6298304187764736000*x^8 - 46823224808407/12496635293184000*x^7 + 15591467870374463/247433378805043200*x^6 - 7259398143917869/10309724116876800*x^5 + 31047590405537630521/6254565964238592000*x^4 - 5294528502460514657/260606915176608000*x^3 + 24145783958576881/579126478170240*x^2 - 11885082074977/383020157520*x + 1
3/2
1/4
0:
1
3/2
1/4
1:
-2*x + 1
3/2
1/4
2:
12/5*x^2 - 32/5*x + 1
3/2
1/4
3:
-72/35*x^3 + 468/35*x^2 - 606/35*x + 1
3/2
1/4
4:
48/35*x^4 - 576/35*x^3 + 1896/35*x^2 - 1648/35*x + 1
3/2
1/4
5:
-288/385*x^5 + 1104/77*x^4 - 6768/77*x^3 + 2184/11*x^2 - 51682/385*x + 1
3/2
1/4
6:
1728/5005*x^6 - 6912/715*x^5 + 94896/1001*x^4 - 399744/1001*x^3 + 320652/455*x^2 - 288048/715*x + 1
3/2
1/4
7:
-3456/25025*x^7 + 1728/325*x^6 - 54432/715*x^5 + 366096/715*x^4 - 5998392/3575*x^3 + 8886252/3575*x^2 - 6320642/5005*x + 1
3/2
1/4
8:
20736/425425*x^8 - 1050624/425425*x^7 + 2951424/60775*x^6 - 1156608/2431*x^5 + 150636192/60775*x^4 - 411251328/60775*x^3 + 340262352/38675*x^2 - 69704416/17017*x + 1
3/2
1/4
9:
-124416/8083075*x^9 + 8024832/8083075*x^8 - 207401472/8083075*x^7 + 397778688/1154725*x^6 - 3007668672/1154725*x^5 + 12978749664/1154725*x^4 - 215710583328/8083075*x^3 + 19495191888/621775*x^2 - 22050984654/1616615*x + 1
3/2
1/4
10:
248832/56581525*x^10 - 3981312/11316305*x^9 + 130823424/11316305*x^8 - 329121792/1616615*x^7 + 17000627328/8083075*x^6 - 1927452672/146965*x^5 + 553395823776/11316305*x^4 - 1176237766656/11316305*x^3 + 374724483516/3328325*x^2 - 10707299776/230945*x + 1
3/2
1/4
11:
-1492992/1301375075*x^11 + 13188096/118306825*x^10 - 107371008/23661365*x^9 + 2399922432/23661365*x^8 - 23173579008/16900975*x^7 + 28108674432/2414425*x^6 - 295436179008/4732273*x^5 + 4898350610208/23661365*x^4 - 47562401862072/118306825*x^3 + 48177936760236/118306825*x^2 - 5955894065866/37182145*x + 1
3/2
1/4
12:
8957952/32534376875*x^12 - 1039122432/32534376875*x^11 + 7464960/4732273*x^10 - 22892544/524875*x^9 + 2208888942336/2957670625*x^8 - 3496386705408/422524375*x^7 + 35611269836544/591534125*x^6 - 169003395343872/591534125*x^5 + 2543818348066032/2957670625*x^4 - 93499597666368/60360625*x^3 + 9648478623597336/6506875375*x^2 - 6133120344816/10935925*x + 1
3/2
1/4
13:
-1990656/32534376875*x^13 + 2985984/357520625*x^12 - 1231220736/2502644375*x^11 + 749979648/45502625*x^10 - 79292929536/227513125*x^9 + 158625361152/32501875*x^8 - 10511142225408/227513125*x^7 + 1926369775872/6500375*x^6 - 289099223602272/227513125*x^5 + 47192614580784/13383125*x^4 - 14907549219476976/2502644375*x^3 + 388391780317224/71504125*x^2 - 369093577957738/185910725*x + 1
3/2
1/4
14:
11943936/943496929375*x^14 - 15925248/7928545625*x^13 + 8957952/64398125*x^12 - 57561808896/10368098125*x^11 + 5820926976/40980625*x^10 - 2310889844736/942554375*x^9 + 193075953046272/6597880625*x^8 - 229531701915648/942554375*x^7 + 8231939534016/5854375*x^6 - 5214815373226752/942554375*x^5 + 148473828275104272/10368098125*x^4 - 237299436417096576/10368098125*x^3 + 130164606610219452/6506875375*x^2 - 38246090214208816/5391411025*x + 1
3/2
1/4
15:
-71663616/29248404810625*x^15 + 2615721984/5849680962125*x^14 - 4293844992/119381244125*x^13 + 108382261248/64282208375*x^12 - 2356602771456/45915863125*x^11 + 6254083021824/5843837125*x^10 - 642822603545088/40906859875*x^9 + 6728737310984448/40906859875*x^8 - 35897916971207808/29219185625*x^7 + 7581143638833984/1168767425*x^6 - 217662431842008864/9183172625*x^5 + 3712149055979404848/64282208375*x^4 - 2571764415603372832104/29248404810625*x^3 + 433028120832762655572/5849680962125*x^2 - 4270374991773593814/167133741775*x + 1
3/2
1/4
16:
143327232/321732452916875*x^16 - 2293235712/24748650224375*x^15 + 551236534272/64346490583375*x^14 - 4283700609024/9192355797625*x^13 + 58841549881344/3535521460625*x^12 - 132534516252672/321411041875*x^11 + 3285934873583616/449975458625*x^10 - 42229722632306688/449975458625*x^9 + 1978984670120566272/2249877293125*x^8 - 101327980899889152/16916370625*x^7 + 20696848253861349888/707104292125*x^6 - 70903769941393394688/707104292125*x^5 + 74530160892646069109568/321732452916875*x^4 - 440135214570018070272/1302560538125*x^3 + 17702641158191555507232/64346490583375*x^2 - 15487633913554712384/167133741775*x + 1
3/2
1/3
0:
1
3/2
1/3
1:
-4/3*x + 1
3/2
1/3
2:
16/15*x^2 - 56/15*x + 1
3/2
1/3
3:
-64/105*x^3 + 176/35*x^2 - 884/105*x + 1
3/2
1/3
4:
256/945*x^4 - 256/63*x^3 + 15776/945*x^2 - 5744/315*x + 1
3/2
1/3
5:
-1024/10395*x^5 + 4864/2079*x^4 - 5248/297*x^3 + 101408/2079*x^2 - 138652/3465*x + 1
3/2
1/3
6:
4096/135135*x^6 - 47104/45045*x^5 + 339200/27027*x^4 - 52480/819*x^3 + 18260464/135135*x^2 - 4080376/45045*x + 1
3/2
1/3
7:
-16384/2027025*x^7 + 4096/10725*x^6 - 29696/4455*x^5 + 348416/6435*x^4 - 4710976/22275*x^3 + 11792912/32175*x^2 - 9559348/45045*x + 1
3/2
1/3
8:
65536/34459425*x^8 - 4063232/34459425*x^7 + 1261568/447525*x^6 - 32776192/984555*x^5 + 1017375232/4922775*x^4 - 3258535424/4922775*x^3 + 3783427136/3828825*x^2 - 6043168/11781*x + 1
3/2
1/3
9:
-262144/654729075*x^9 + 65536/2078505*x^8 - 215810048/218243025*x^7 + 166117376/10392525*x^6 - 4491483136/31177575*x^5 + 1520098816/2078505*x^4 - 1314638256896/654729075*x^3 + 9237363008/3464175*x^2 - 18520631732/14549535*x + 1
3/2
1/3
10:
1048576/13749310575*x^10 - 524288/70509285*x^9 + 271384576/916620705*x^8 - 273809408/43648605*x^7 + 50596323328/654729075*x^6 - 2755702784/4849845*x^5 + 615710884352/249987465*x^4 - 5478567619072/916620705*x^3 + 11037463130704/1527701175*x^2 - 9391301944/2909907*x + 1
3/2
1/3
11:
-4194304/316234143225*x^11 + 45088768/28748558475*x^10 - 29622272/383314113*x^9 + 796196864/383314113*x^8 - 45857472512/1368978975*x^7 + 27056955392/80528175*x^6 - 2418335979520/1149942339*x^5 + 9222207360512/1149942339*x^4 - 168537004689728/9582852825*x^3 + 3308184443728/168120225*x^2 - 557242120196/66927861*x + 1
3/2
1/3
12:
16777216/7905853580625*x^12 - 788529152/2635284526875*x^11 + 2097152/117341055*x^10 - 28461498368/47914264125*x^9 + 2908101738496/239571320625*x^8 - 86446309376/543245625*x^7 + 194840952553472/143742792375*x^6 - 356388099284992/47914264125*x^5 + 2618531455601408/102673423125*x^4 - 12310921822775552/239571320625*x^3 + 9466739871053152/175685635125*x^2 - 36453304298288/1673196525*x + 1
3/2
1/3
13:
-67108864/213458046676875*x^13 + 16777216/321957838125*x^12 - 60909682688/16419849744375*x^11 + 782237696/5237591625*x^10 - 1875988185088/497571204375*x^9 + 1152605421568/18428563125*x^8 - 1037375757942784/1492713613125*x^7 + 515091066339328/99514240875*x^6 - 37979237624357888/1492713613125*x^5 + 39676257163642112/497571204375*x^4 - 272758091395106432/1824427749375*x^3 + 18041277884447392/121628516625*x^2 - 289538666884868/5019589575*x + 1
3/2
1/3
14:
268435456/6190283353629375*x^14 - 134217728/16078658061375*x^13 + 2499805184/3580267989375*x^12 - 2277624512512/68025091798125*x^11 + 12332302336/12054774375*x^10 - 375351934976/17924925375*x^9 + 12725796775591936/43288694780625*x^8 - 766316635881472/268873880625*x^7 + 117259562914820096/6184099254375*x^6 - 912762839877632/10754955225*x^5 + 5583456855136769792/22675030599375*x^4 - 17536214583357184/40418949375*x^3 + 648778788553860112/1581170716125*x^2 - 22450584229239784/145568097675*x + 1
3/2
1/3
15:
-1073741824/191898783962510625*x^15 + 15837691904/12793252264167375*x^14 - 4093640704/34054797508875*x^13 + 951654023168/140585189716125*x^12 - 30534998687744/124045755631875*x^11 + 77863167459328/12780471792375*x^10 - 28287616317390848/268389907639875*x^9 + 115303136755908608/89463302546625*x^8 - 112365209989562368/10089846151875*x^7 + 859695260042104832/12780471792375*x^6 - 117107566258318363648/421755569148375*x^5 + 6230212840510118144/8269717042125*x^4 - 26808754663757244121024/21322087106945625*x^3 + 1620633807911285591504/1421472473796375*x^2 - 1876501576103427412/4512611027925*x + 1
3/2
1/3
16:
4294967296/6332659870762850625*x^16 - 17179869184/100518410647029375*x^15 + 371514671104/19485107294654925*x^14 - 333933707264/268049095058745*x^13 + 528523844386816/9941381272783125*x^12 - 1099836367568896/702925948580625*x^11 + 289559830706782208/8856866952115875*x^10 - 13832385527283712/28117037943225*x^9 + 237007606025197060096/44284334760579375*x^8 - 1090554209150697472/26034294391875*x^7 + 462599161196144459776/1988276254556625*x^6 - 276749656451446718464/309287417375475*x^5 + 1610525614179980466584576/703628874529205625*x^4 - 167361712180449297408/45961778988125*x^3 + 3825888681463733964928/1202784400904625*x^2 - 5096138845805657152/4512611027925*x + 1
3/2
1/2
0:
1
3/2
1/2
1:
-2/3*x + 1
3/2
1/2
2:
4/15*x^2 - 8/5*x + 1
3/2
1/2
3:
-8/105*x^3 + 36/35*x^2 - 62/21*x + 1
3/2
1/2
4:
16/945*x^4 - 128/315*x^3 + 2552/945*x^2 - 224/45*x + 1
3/2
1/2
5:
-32/10395*x^5 + 80/693*x^4 - 2864/2079*x^3 + 4184/693*x^2 - 9362/1155*x + 1
3/2
1/2
6:
64/135135*x^6 - 128/5005*x^5 + 12944/27027*x^4 - 34240/9009*x^3 + 1678156/135135*x^2 - 53528/4095*x + 1
3/2
1/2
7:
-128/2027025*x^7 + 448/96525*x^6 - 7264/57915*x^5 + 30256/19305*x^4 - 2702696/289575*x^3 + 71284/2925*x^2 - 73286/3465*x + 1
3/2
1/2
8:
256/34459425*x^8 - 8192/11486475*x^7 + 25856/984555*x^6 - 155648/328185*x^5 + 21944992/4922775*x^4 - 11657728/546975*x^3 + 106927376/2297295*x^2 - 26475776/765765*x + 1
3/2
1/2
9:
-512/654729075*x^9 + 768/8083075*x^8 - 997888/218243025*x^7 + 1170176/10392525*x^6 - 47734208/31177575*x^5 + 120238304/10392525*x^4 - 30372234976/654729075*x^3 + 6367640528/72747675*x^2 - 49030442/855855*x + 1
3/2
1/2
10:
1024/13749310575*x^10 - 2048/183324141*x^9 + 623872/916620705*x^8 - 956416/43648605*x^7 + 266092672/654729075*x^6 - 64665856/14549535*x^5 + 77489519584/2749862115*x^4 - 89565340544/916620705*x^3 + 22672134236/138881925*x^2 - 5673832/58905*x + 1
3/2
1/2
11:
-2048/316234143225*x^11 + 11264/9582852825*x^10 - 169472/1916570565*x^9 + 65792/18253053*x^8 - 6297856/72051525*x^7 + 66110848/50702925*x^6 - 5290553152/442285515*x^5 + 25131088288/383314113*x^4 - 1927747030696/9582852825*x^3 + 46135379428/152108775*x^2 - 54978898262/334639305*x + 1
3/2
1/2
12:
4096/7905853580625*x^12 - 32768/292809391875*x^11 + 22528/2211427575*x^10 - 24567808/47914264125*x^9 + 3771563776/239571320625*x^8 - 3502206976/11408158125*x^7 + 552027114752/143742792375*x^6 - 486127657984/15971421375*x^5 + 105974685065936/718713961875*x^4 - 5138291909248/12609016875*x^3 + 98902236604552/175685635125*x^2 - 20660517536/72747675*x + 1
3/2
1/2
13:
-8192/213458046676875*x^13 + 53248/5473283248125*x^12 - 692224/656793989775*x^11 + 6387712/99514240875*x^10 - 1210709504/497571204375*x^9 + 1106868992/18428563125*x^8 - 293119779328/298542722625*x^7 + 1055281211648/99514240875*x^6 - 110766697690144/1492713613125*x^5 + 160822274658448/497571204375*x^4 - 297761702412368/364885549875*x^3 + 1496142566984/1430923725*x^2 - 498840079106/1003917915*x + 1
3/2
1/2
14:
16384/6190283353629375*x^14 - 32768/42110771113125*x^13 + 6729728/68025091798125*x^12 - 162578432/22675030599375*x^11 + 677837824/2061366418125*x^10 - 764930048/76346904375*x^9 + 8971378586368/43288694780625*x^8 - 6025853843456/2061366418125*x^7 + 172229346509504/6184099254375*x^6 - 360688368716672/2061366418125*x^5 + 5250453452711312/7558343533125*x^4 - 10443081804608/6443600625*x^3 + 113917420148348/58561878375*x^2 - 42636778099304/48522699225*x + 1
3/2
1/2
15:
-32768/191898783962510625*x^15 + 16384/284294494759275*x^14 - 4235264/498438399902625*x^13 + 5976064/8269717042125*x^12 - 83155367936/2108777845741875*x^11 + 18573673472/12780471792375*x^10 - 9955482961408/268389907639875*x^9 + 19733196083456/29821100848875*x^8 - 1577187602140544/191707076885625*x^7 + 898380316139456/12780471792375*x^6 - 169473571245824288/421755569148375*x^5 + 206689663194024848/140585189716125*x^4 - 9298806943663864/2906104280625*x^3 + 5155894329229170988/1421472473796375*x^2 - 244065819923206/155607276825*x + 1
3/2
1/2
16:
65536/6332659870762850625*x^16 - 8388608/2110886623587616875*x^15 + 851836928/1266531974152570125*x^14 - 114294784/1723172753949075*x^13 + 12848513024/3025637778673125*x^12 - 130864381952/702925948580625*x^11 + 50890081132544/8856866952115875*x^10 - 14929537859584/118091559361545*x^9 + 5175134580505088/2604960868269375*x^8 - 46668530678923264/2108777845741875*x^7 + 2391313846806748672/13917933781896375*x^6 - 18627214356533248/20619161158365*x^5 + 127242155355125138368/41389933795835625*x^4 - 25884467367453650944/4114788739936875*x^3 + 106016734264219605088/15636197211760125*x^2 - 410890830655744/145568097675*x + 1
3/2
2/3
0:
1
3/2
2/3
1:
-1/3*x + 1
3/2
2/3
2:
1/15*x^2 - 11/15*x + 1
3/2
2/3
3:
-1/105*x^3 + 8/35*x^2 - 128/105*x + 1
3/2
2/3
4:
1/945*x^4 - 2/45*x^3 + 71/135*x^2 - 572/315*x + 1
3/2
2/3
5:
-1/10395*x^5 + 13/2079*x^4 - 271/2079*x^3 + 2111/2079*x^2 - 8863/3465*x + 1
3/2
2/3
6:
1/135135*x^6 - 31/45045*x^5 + 86/3861*x^4 - 2771/9009*x^3 + 240124/135135*x^2 - 157249/45045*x + 1
3/2
2/3
7:
-1/2027025*x^7 + 2/32175*x^6 - 167/57915*x^5 + 133/2145*x^4 - 184957/289575*x^3 + 94063/32175*x^2 - 210688/45045*x + 1
3/2
2/3
8:
1/34459425*x^8 - 164/34459425*x^7 + 134/447525*x^6 - 140/15147*x^5 + 66527/447525*x^4 - 6004508/4922775*x^3 + 17669858/3828825*x^2 - 949792/153153*x + 1
3/2
2/3
9:
-1/654729075*x^9 + 23/72747675*x^8 - 514/19840275*x^7 + 11282/10392525*x^6 - 782539/31177575*x^5 + 3349571/10392525*x^4 - 1438148438/654729075*x^3 + 171634922/24249225*x^2 - 119010341/14549535*x + 1
3/2
2/3
10:
1/13749310575*x^10 - 1/53918865*x^9 + 1759/916620705*x^8 - 4574/43648605*x^7 + 2155093/654729075*x^6 - 885113/14549535*x^5 + 1787873623/2749862115*x^4 - 3473538646/916620705*x^3 + 16245843319/1527701175*x^2 - 156706163/14549535*x + 1
3/2
2/3
11:
-1/316234143225*x^11 + 4/4106936925*x^10 - 2/16105635*x^9 + 16417/1916570565*x^8 - 2173/6194475*x^7 + 12066094/1368978975*x^6 - 8213830/60523281*x^5 + 60037451/48316905*x^4 - 8665118171/1368978975*x^3 + 3867789094/245714175*x^2 - 4749665944/334639305*x + 1
3/2
2/3
12:
1/7905853580625*x^12 - 122/2635284526875*x^11 + 41/5749711695*x^10 - 29048/47914264125*x^9 + 7515706/239571320625*x^8 - 3909502/3802719375*x^7 + 3095068397/143742792375*x^6 - 801174536/2818486125*x^5 + 125926424282/55285689375*x^4 - 2470510919222/239571320625*x^3 + 4049512518127/175685635125*x^2 - 1845591604/98423325*x + 1
3/2
2/3
13:
-1/213458046676875*x^13 + 1/497571204375*x^12 - 863/2345692820625*x^11 + 3761/99514240875*x^10 - 1199602/497571204375*x^9 + 1840204/18428563125*x^8 - 4073029123/1492713613125*x^7 + 4877932693/99514240875*x^6 - 120840660566/213244801875*x^5 + 87397122892/21633530625*x^4 - 30059335013909/1824427749375*x^3 + 19489237931/581954625*x^2 - 124817992721/5019589575*x + 1
3/2
2/3
14:
1/6190283353629375*x^14 - 71/884326193375625*x^13 + 1172/68025091798125*x^12 - 20443/9717870256875*x^11 + 111427/687122139375*x^10 - 17070572/2061366418125*x^9 + 12382556197/43288694780625*x^8 - 41469200663/6184099254375*x^7 + 652553324291/6184099254375*x^6 - 959230527916/883442750625*x^5 + 158222311874699/22675030599375*x^4 - 606542148983/23400444375*x^3 + 4026665003674/83219511375*x^2 - 40519003313/1223261325*x + 1
3/2
2/3
15:
-1/191898783962510625*x^15 + 2/673329066535125*x^14 - 4049/5482822398928875*x^13 + 193/1825781684625*x^12 - 20426512/2108777845741875*x^11 + 7640203/12780471792375*x^10 - 6833679473/268389907639875*x^9 + 67510677386/89463302546625*x^8 - 2971097905288/191707076885625*x^7 + 79275432457/365156336925*x^6 - 44710300660807/22197661534125*x^5 + 1658114393053186/140585189716125*x^4 - 858771692754314791/21322087106945625*x^3 + 8998868114680111/129224770345125*x^2 - 28586547820504/644658718275*x + 1
3/2
2/3
16:
1/6332659870762850625*x^16 - 8/78180986058800625*x^15 + 36956/1266531974152570125*x^14 - 97288/20103682129405875*x^13 + 36178942/69589668909481875*x^12 - 26810864/702925948580625*x^11 + 17389779608/8856866952115875*x^10 - 23538612952/328032109337625*x^9 + 82511511983821/44284334760579375*x^8 - 1408599370768/41348585210625*x^7 + 5988733270357384/13917933781896375*x^6 - 5625317703028456/1546437086877375*x^5 + 810534578564448058/41389933795835625*x^4 - 4844312777955979112/78180986058800625*x^3 + 1562995419530248276/15636197211760125*x^2 - 38469309853024/644658718275*x + 1
3/2
3/4
0:
1
3/2
3/4
1:
-2/9*x + 1
3/2
3/4
2:
4/135*x^2 - 64/135*x + 1
3/2
3/4
3:
-8/2835*x^3 + 92/945*x^2 - 2158/2835*x + 1
3/2
3/4
4:
16/76545*x^4 - 64/5103*x^3 + 16376/76545*x^2 - 27824/25515*x + 1
3/2
3/4
5:
-32/2525985*x^5 + 592/505197*x^4 - 17648/505197*x^3 + 198584/505197*x^2 - 1238086/841995*x + 1
3/2
3/4
6:
64/98513415*x^6 - 256/2985255*x^5 + 11120/2814669*x^4 - 56960/729729*x^3 + 64252876/98513415*x^2 - 62765104/32837805*x + 1
3/2
3/4
7:
-128/4433103675*x^7 + 1088/211100175*x^6 - 42976/126660105*x^5 + 39856/3838185*x^4 - 96921896/633300525*x^3 + 71323204/70366725*x^2 - 239008886/98513415*x + 1
3/2
3/4
8:
256/226088287425*x^8 - 59392/226088287425*x^7 + 755968/32298326775*x^6 - 6620672/6459665355*x^5 + 757389472/32298326775*x^4 - 8886204544/32298326775*x^3 + 12606787792/8373640275*x^2 - 3045288032/1004836833*x + 1
3/2
3/4
9:
-512/12887032383225*x^9 + 256/22029115185*x^8 - 40448/30039702525*x^7 + 5445376/68185356525*x^6 - 1606305728/613668208725*x^5 + 651493984/13637071305*x^4 - 5992910309728/12887032383225*x^3 + 3098935805104/1431892487025*x^2 - 1072322623786/286378497405*x + 1
3/2
3/4
10:
1024/811883040143175*x^10 - 8192/18041845336515*x^9 + 3591424/54125536009545*x^8 - 1466368/286378497405*x^7 + 8794579072/38661097149675*x^6 - 5115563008/859135492215*x^5 + 14668376175328/162376608028635*x^4 - 13545352270336/18041845336515*x^3 + 273864788631796/90209226682575*x^2 - 2247917536/489535893*x + 1
3/2
3/4
11:
-2048/56019929769879075*x^11 + 80896/5092720888170825*x^10 - 194048/67902945175611*x^9 + 18892544/67902945175611*x^8 - 3901874944/242510518484325*x^7 + 138526427008/242510518484325*x^6 - 2534433501248/203708835526833*x^5 + 32887586938016/203708835526833*x^4 - 662089749565112/565857876463425*x^3 + 2365062459664204/565857876463425*x^2 - 22145335823474/3952023264189*x + 1
3/2
3/4
12:
4096/4201494732740930625*x^12 - 704512/1400498244246976875*x^11 + 333824/3055632532902495*x^10 - 37056512/2829289382317125*x^9 + 121701035776/127318022204270625*x^8 - 38275463168/866108994586875*x^7 + 99790174821632/76390813322562375*x^6 - 620247571799552/25463604440854125*x^5 + 8111524155437072/29381082047139375*x^4 - 75265581832314304/42439340734756875*x^3 + 529481560289919112/93366549616465125*x^2 - 2020619218159376/296401744814175*x + 1
3/2
3/4
13:
-8192/340321073352015380625*x^13 + 126976/8726181368000394375*x^12 - 610304/162599652819883125*x^11 + 86198272/158657843054552625*x^10 - 38740657664/793289215272763125*x^9 + 83741913344/29381082047139375*x^8 - 261200468091392/2379867645818289375*x^7 + 440905313371904/158657843054552625*x^6 - 15400647263126752/339981092259755625*x^5 + 361529023225627696/793289215272763125*x^4 - 7646107328066020816/2908727122666798125*x^3 + 1475093254299361496/193915141511119875*x^2 - 66265329058275034/8002847109982725*x + 1
3/2
3/4
14:
16384/29607933381625338114375*x^14 - 65536/169188190752144789225*x^13 + 2240512/19138935605446243125*x^12 - 344686592/17124310804872954375*x^11 + 55092224/25215988939981875*x^10 - 309741744128/1971890335106582625*x^9 + 1581385263979264/207048485186191175625*x^8 - 7454078035431424/29578355026598739375*x^7 + 165068945438884544/29578355026598739375*x^6 - 478029518064645376/5915671005319747875*x^5 + 79271480521757090608/108453968430862044375*x^4 - 138309461426979208832/36151322810287348125*x^3 + 76469637463377068948/7562690518933675125*x^2 - 6998784779758969136/696247698568497075*x + 1
3/2
3/4
15:
-32768/2753537804491156444636875*x^15 + 1753088/183569186966077096309125*x^14 - 262955008/78672508699747326989625*x^13 + 50311168/74712733807927186125*x^12 - 375355394048/4322665313172930054375*x^11 + 197525562368/26197971594987454875*x^10 - 1739498933095936/3851101824463155866625*x^9 + 24163106274550016/1283700608154385288875*x^8 - 87919578621058432/161811001027863691875*x^7 + 653629467831387328/61128600388304061375*x^6 - 5235663010010486176/37588394027590696125*x^5 + 329850796339750501328/288177687544862003625*x^4 - 1678143880052656201941368/305948644943461827181875*x^3 + 272168216422416106030228/20396576329564121812125*x^2 - 41602842573889143986/3407949261414222525*x + 1
3/2
3/4
16:
65536/272600242644624488019050625*x^16 - 1048576/4782460397274113824895625*x^15 + 73793536/838769977368075347750925*x^14 - 10659037184/519238557418332358131525*x^13 + 9292254625792/2995607062028840527681875*x^12 - 420999790592/1315593790965674364375*x^11 + 8828265750683648/381259080621852430795875*x^10 - 41686237134848/35058306264078384441*x^9 + 82652404277700123136/1906295403109262153979375*x^8 - 14426844401695748096/12967995939518790163125*x^7 + 11804451232860191882752/599121412405768105536375*x^6 - 69024726853636240384/295862425879391657055*x^5 + 53213265576853792402529216/30288915849402720891005625*x^4 - 26135222175269020676071168/3365435094378080099000625*x^3 + 906517742396698094353888/51775924528893539984625*x^2 - 2882802784235647667392/194253107900610683925*x + 1
2
1/4
0:
1
2
1/4
1:
-3/2*x + 1
2
1/4
2:
3/2*x^2 - 9/2*x + 1
2
1/4
3:
-9/8*x^3 + 63/8*x^2 - 45/4*x + 1
2
1/4
4:
27/40*x^4 - 171/20*x^3 + 1197/40*x^2 - 561/20*x + 1
2
1/4
5:
-27/80*x^5 + 27/4*x^4 - 693/16*x^3 + 411/4*x^2 - 1467/20*x + 1
2
1/4
6:
81/560*x^6 - 2349/560*x^5 + 4779/112*x^4 - 20907/112*x^3 + 11979/35*x^2 - 28449/140*x + 1
2
1/4
7:
-243/4480*x^7 + 1377/640*x^6 - 20331/640*x^5 + 28215/128*x^4 - 59607/80*x^3 + 181917/160*x^2 - 166083/280*x + 1
2
1/4
8:
81/4480*x^8 - 1053/1120*x^7 + 1215/64*x^6 - 7641/40*x^5 + 653967/640*x^4 - 457821/160*x^3 + 852807/224*x^2 - 505863/280*x + 1
2
1/4
9:
-243/44800*x^9 + 8019/22400*x^8 - 212139/22400*x^7 + 208251/1600*x^6 - 6446061/6400*x^5 + 14223033/3200*x^4 - 120687543/11200*x^3 + 72205209/5600*x^2 - 1593243/280*x + 1
2
1/4
10:
729/492800*x^10 - 1701/14080*x^9 + 99873/24640*x^8 - 3591783/49280*x^7 + 54115371/70400*x^6 - 68858181/14080*x^5 + 915900939/49280*x^4 - 141481053/3520*x^3 + 2721713103/61600*x^2 - 56672193/3080*x + 1
2
1/4
11:
-729/1971200*x^11 + 6561/179200*x^10 - 243/160*x^9 + 619893/17920*x^8 - 85377807/179200*x^7 + 105465159/25600*x^6 - 402863787/17920*x^5 + 678904011/8960*x^4 - 477756009/3200*x^3 + 214316517/1400*x^2 - 187161363/3080*x + 1
2
1/4
12:
2187/25625600*x^12 - 129033/12812800*x^11 + 168399/332800*x^10 - 663147/46592*x^9 + 577513071/2329600*x^8 - 3253309029/1164800*x^7 + 48105590499/2329600*x^6 - 23180601789/232960*x^5 + 25273908279/83200*x^4 - 161297145567/291200*x^3 + 107245032471/200200*x^2 - 8174630439/40040*x + 1
2
1/4
13:
-6561/358758400*x^13 + 2187/862400*x^12 - 837621/5519360*x^11 + 809919/156800*x^10 - 278343621/2508800*x^9 + 123695991/78400*x^8 - 1521388737/100352*x^7 + 15467754087/156800*x^6 - 134433763209/313600*x^5 + 94408447617/78400*x^4 - 709209185499/344960*x^3 + 407749453623/215600*x^2 - 27859894059/40040*x + 1
2
1/4
14:
6561/1793792000*x^14 - 150903/256256000*x^13 + 815751/19712000*x^12 - 33037551/19712000*x^11 + 77964363/1792000*x^10 - 1365096483/1792000*x^9 + 115655876001/12544000*x^8 - 139352748543/1792000*x^7 + 6366789297/14000*x^6 - 405586732437/224000*x^5 + 5835757925961/1232000*x^4 - 9413883009261/1232000*x^3 + 18861731214609/2802800*x^2 - 13728878469/5720*x + 1
2
1/4
15:
-19683/28700672000*x^15 + 728271/5740134400*x^14 - 8483373/820019200*x^13 + 2819043/5734400*x^12 - 4784003451/315392000*x^11 + 52516431/163840*x^10 - 191408008311/40140800*x^9 + 2029062942423/40140800*x^8 - 684803515509/1792000*x^7 + 1462776228099/716800*x^6 - 29708838383391/3942400*x^5 + 10438193879829/563200*x^4 - 6379445255793669/224224000*x^3 + 49153840752897/2038400*x^2 - 95700014307/11440*x + 1
2
1/4
16:
59049/487911424000*x^16 - 1554957/60988928000*x^15 + 5294727/2217779200*x^14 - 114600987/871270400*x^13 + 12753768249/2680832000*x^12 - 19997956431/167552000*x^11 + 365040597969/170598400*x^10 - 1186932237129/42649600*x^9 + 900253573082919/3411968000*x^8 - 110679054984711/60928000*x^7 + 48083118063039/5361664*x^6 - 519620759386011/16755200*x^5 + 200291793798705291/2772224000*x^4 - 404638449683438403/3811808000*x^3 + 33142388218816599/381180800*x^2 - 5721435719679/194480*x + 1
2
1/3
0:
1
2
1/3
1:
-x + 1
2
1/3
2:
2/3*x^2 - 8/3*x + 1
2
1/3
3:
-1/3*x^3 + 3*x^2 - 17/3*x + 1
2
1/3
4:
2/15*x^4 - 32/15*x^3 + 142/15*x^2 - 172/15*x + 1
2
1/3
5:
-2/45*x^5 + 10/9*x^4 - 80/9*x^3 + 236/9*x^2 - 117/5*x + 1
2
1/3
6:
4/315*x^6 - 16/35*x^5 + 362/63*x^4 - 216/7*x^3 + 21676/315*x^2 - 1724/35*x + 1
2
1/3
7:
-1/315*x^7 + 7/45*x^6 - 127/45*x^5 + 215/9*x^4 - 4387/45*x^3 + 7963/45*x^2 - 3769/35*x + 1
2
1/3
8:
2/2835*x^8 - 128/2835*x^7 + 452/405*x^6 - 5528/405*x^5 + 35594/405*x^4 - 118376/405*x^3 + 47588/105*x^2 - 76936/315*x + 1
2
1/3
9:
-2/14175*x^9 + 2/175*x^8 - 1744/4725*x^7 + 1384/225*x^6 - 38618/675*x^5 + 67486/225*x^4 - 12055048/14175*x^3 + 1835032/1575*x^2 - 36047/63*x + 1
2
1/3
10:
4/155925*x^10 - 16/6237*x^9 + 218/2079*x^8 - 23728/10395*x^7 + 214672/7425*x^6 - 324728/1485*x^5 + 6081410/6237*x^4 - 75851416/31185*x^3 + 5806714/1925*x^2 - 4772288/3465*x + 1
2
1/3
11:
-2/467775*x^11 + 22/42525*x^10 - 74/2835*x^9 + 2038/2835*x^8 - 168472/14175*x^7 + 247576/2025*x^6 - 6674992/8505*x^5 + 26095276/8505*x^4 - 97661509/14175*x^3 + 37206823/4725*x^2 - 11747123/3465*x + 1
2
1/3
12:
4/6081075*x^12 - 64/675675*x^11 + 3196/552825*x^10 - 1448/7371*x^9 + 756634/184275*x^8 - 3382672/61425*x^7 + 265335328/552825*x^6 - 11032096/4095*x^5 + 5219565284/552825*x^4 - 3577899112/184275*x^3 + 14005283954/675675*x^2 - 382889084/45045*x + 1
2
1/3
13:
-4/42567525*x^13 + 52/3274425*x^12 - 3776/3274425*x^11 + 14104/297675*x^10 - 13462/11025*x^9 + 2052262/99225*x^8 - 69859168/297675*x^7 + 531240592/297675*x^6 - 2664857588/297675*x^5 + 8514719732/297675*x^4 - 59581337192/1091475*x^3 + 20008082516/363825*x^2 - 139253987/6435*x + 1
2
1/3
14:
8/638512875*x^14 - 32/13030875*x^13 + 1468/7016625*x^12 - 71728/7016625*x^11 + 67688/212625*x^10 - 1412408/212625*x^9 + 424516838/4465125*x^8 - 599364464/637875*x^7 + 4063523608/637875*x^6 - 18522251008/637875*x^5 + 66817650212/779625*x^4 - 119568857552/779625*x^3 + 231709661504/1576575*x^2 - 502738972/9009*x + 1
2
1/3
15:
-1/638512875*x^15 + 1/2837835*x^14 - 127/3648645*x^13 + 311/155925*x^12 - 517987/7016625*x^11 + 5273/2835*x^10 - 1170179/35721*x^9 + 40464311/99225*x^8 - 326811259/91125*x^7 + 12495401/567*x^6 - 25954262087/280665*x^5 + 39724278211/155925*x^4 - 30580078072541/70945875*x^3 + 41556866623/105105*x^2 - 6553357487/45045*x + 1
2
1/3
16:
2/10854718875*x^16 - 512/10854718875*x^15 + 11608/2170943775*x^14 - 110128/310134825*x^13 + 1837604/119282625*x^12 - 54988784/119282625*x^11 + 148697608/15181425*x^10 - 2275189936/15181425*x^9 + 125819673362/75907125*x^8 - 142979337776/10843875*x^7 + 1774673067128/23856525*x^6 - 6927155404976/23856525*x^5 + 908163766859252/1206079875*x^4 - 1462432138763152/1206079875*x^3 + 1147187448632/1072071*x^2 - 293191985584/765765*x + 1
2
1/2
0:
1
2
1/2
1:
-1/2*x + 1
2
1/2
2:
1/6*x^2 - 7/6*x + 1
2
1/2
3:
-1/24*x^3 + 5/8*x^2 - 25/12*x + 1
2
1/2
4:
1/120*x^4 - 13/60*x^3 + 191/120*x^2 - 203/60*x + 1
2
1/2
5:
-1/720*x^5 + 1/18*x^4 - 103/144*x^3 + 31/9*x^2 - 317/60*x + 1
2
1/2
6:
1/5040*x^6 - 19/1680*x^5 + 227/1008*x^4 - 215/112*x^3 + 4313/630*x^2 - 3419/420*x + 1
2
1/2
7:
-1/40320*x^7 + 11/5760*x^6 - 313/5760*x^5 + 829/1152*x^4 - 3299/720*x^3 + 18671/1440*x^2 - 10543/840*x + 1
2
1/2
8:
1/362880*x^8 - 5/18144*x^7 + 55/5184*x^6 - 163/810*x^5 + 103567/51840*x^4 - 26345/2592*x^3 + 48143/2016*x^2 - 49199/2520*x + 1
2
1/2
9:
-1/3628800*x^9 + 1/28800*x^8 - 1051/604800*x^7 + 643/14400*x^6 - 109909/172800*x^5 + 145709/28800*x^4 - 19489601/907200*x^3 + 311731/7200*x^2 - 77563/2520*x + 1
2
1/2
10:
1/39916800*x^10 - 31/7983360*x^9 + 163/665280*x^8 - 10897/1330560*x^7 + 300673/1900800*x^6 - 687139/380160*x^5 + 47988467/3991680*x^4 - 87700607/1995840*x^3 + 43168303/554400*x^2 - 273253/5544*x + 1
2
1/2
11:
-1/479001600*x^11 + 17/43545600*x^10 - 11/362880*x^9 + 53/41472*x^8 - 466301/14515200*x^7 + 1032701/2073600*x^6 - 20735383/4354560*x^5 + 11882971/435456*x^4 - 159415369/1814400*x^3 + 1507541/10800*x^2 - 444739/5544*x + 1
2
1/2
12:
1/6227020800*x^12 - 37/1037836800*x^11 + 1891/566092800*x^10 - 3271/18869760*x^9 + 1037311/188697600*x^8 - 1163009/10483200*x^7 + 814849873/566092800*x^6 - 223803029/18869760*x^5 + 8474783819/141523200*x^4 - 4078792663/23587200*x^3 + 1352489923/5405400*x^2 - 9559843/72072*x + 1
2
1/2
13:
-1/87178291200*x^13 + 1/335301120*x^12 - 89/268240896*x^11 + 3167/152409600*x^10 - 54949/67737600*x^9 + 209863/10160640*x^8 - 42536717/121927680*x^7 + 594464021/152409600*x^6 - 539279311/19051200*x^5 + 195251821/1524096*x^4 - 9405702331/27941760*x^3 + 2615617139/5821200*x^2 - 16041967/72072*x + 1
2
1/2
14:
1/1307674368000*x^14 - 43/186810624000*x^13 + 431/14370048000*x^12 - 32051/14370048000*x^11 + 45761/435456000*x^10 - 1434301/435456000*x^9 + 641812441/9144576000*x^8 - 1334201923/1306368000*x^7 + 1641665017/163296000*x^6 - 10672154287/163296000*x^5 + 80475783937/299376000*x^4 - 21631900303/33264000*x^3 + 61244111231/75675600*x^2 - 136412267/360360*x + 1
2
1/2
15:
-1/20922789888000*x^15 + 23/1394852659200*x^14 - 1487/597793996800*x^13 + 41/189235200*x^12 - 2786857/229920768000*x^11 + 127777/278691840*x^10 - 351879869/29262643200*x^9 + 2152707551/9754214400*x^8 - 3692324353/1306368000*x^7 + 1446033209/58060800*x^6 - 422447999749/2874009600*x^5 + 532347316091/958003200*x^4 - 22699973571907/18162144000*x^3 + 885651415819/605404800*x^2 - 469578091/720720*x + 1
2
1/2
16:
1/355687428096000*x^16 - 1/907365888000*x^15 + 3389/17784371404800*x^14 - 2441/127031224320*x^13 + 2460641/1954326528000*x^12 - 3453341/61072704000*x^11 + 222551297/124366233600*x^10 - 35901653/888330240*x^9 + 1623129179311/2487324672000*x^8 - 47442552601/6345216000*x^7 + 5839690263023/97716326400*x^6 - 790860023647/2442908160*x^5 + 8413864477963643/7410154752000*x^4 - 105591110484437/44108064000*x^3 + 27321475444493/10291881600*x^2 - 13886154977/12252240*x + 1
2
2/3
0:
1
2
2/3
1:
-1/4*x + 1
2
2/3
2:
1/24*x^2 - 13/24*x + 1
2
2/3
3:
-1/192*x^3 + 9/64*x^2 - 85/96*x + 1
2
2/3
4:
1/1920*x^4 - 23/960*x^3 + 611/1920*x^2 - 1243/960*x + 1
2
2/3
5:
-1/23040*x^5 + 7/2304*x^4 - 319/4608*x^3 + 1391/2304*x^2 - 143/80*x + 1
2
2/3
6:
1/322560*x^6 - 11/35840*x^5 + 689/64512*x^4 - 1153/7168*x^3 + 167297/161280*x^2 - 10693/4480*x + 1
2
2/3
7:
-1/5160960*x^7 + 19/737280*x^6 - 937/737280*x^5 + 4325/147456*x^4 - 30299/92160*x^3 + 308599/184320*x^2 - 111949/35840*x + 1
2
2/3
8:
1/92897280*x^8 - 43/23224320*x^7 + 163/1327104*x^6 - 6677/1658880*x^5 + 920407/13271040*x^4 - 2049301/3317760*x^3 + 445717/172032*x^2 - 2605427/645120*x + 1
2
2/3
9:
-1/1857945600*x^9 + 1/8601600*x^8 - 3091/309657600*x^7 + 203/460800*x^6 - 955309/88473600*x^5 + 546571/3686400*x^4 - 508108151/464486400*x^3 + 3139151/806400*x^2 - 3346097/645120*x + 1
2
2/3
10:
1/40874803200*x^10 - 53/8174960640*x^9 + 953/1362493440*x^8 - 54479/1362493440*x^7 + 2571733/1946419200*x^6 - 10062593/389283840*x^5 + 301285289/1021870080*x^4 - 3791818519/2043740160*x^3 + 541813133/94617600*x^2 - 1472771/221760*x + 1
2
2/3
11:
-1/980995276800*x^11 + 29/89181388800*x^10 - 1/23224320*x^9 + 9199/2972712960*x^8 - 3940061/29727129600*x^7 + 14860217/4246732800*x^6 - 507870283/8918138880*x^5 + 2476369169/4459069440*x^4 - 11317506649/3715891200*x^3 + 2568610903/309657600*x^2 - 241305433/28385280*x + 1
2
2/3
12:
1/25505877196800*x^12 - 1/67475865600*x^11 + 5479/2318716108800*x^10 - 3223/15458107392*x^9 + 8681311/772905369600*x^8 - 49543373/128817561600*x^7 + 19602051397/2318716108800*x^6 - 433488329/3680501760*x^5 + 581508536669/579679027200*x^4 - 471047111987/96613171200*x^3 + 1052311126003/88562073600*x^2 - 8044421123/738017280*x + 1
2
2/3
13:
-1/714164561510400*x^13 + 17/27467867750400*x^12 - 257/2197429420032*x^11 + 31037/2497078886400*x^10 - 456329/554906419200*x^9 + 29490827/832359628800*x^8 - 1009420397/998831554560*x^7 + 47520635051/2497078886400*x^6 - 289434956213/1248539443200*x^5 + 1094362357993/624269721600*x^4 - 875845584203/114449448960*x^3 + 100641405629/5960908800*x^2 - 5173555069/369008640*x + 1
2
2/3
14:
1/21424936845312000*x^14 - 73/3060705263616000*x^13 + 1241/235438866432000*x^12 - 156341/235438866432000*x^11 + 377611/7134511104000*x^10 - 19986451/7134511104000*x^9 + 15068613991/149824733184000*x^8 - 52625961013/21403533312000*x^7 + 433501081753/10701766656000*x^6 - 2346383728859/5350883328000*x^5 + 361266796489/121110528000*x^4 - 4833724252891/408748032000*x^3 + 3286024903043/137763225600*x^2 - 26730412867/1476034560*x + 1
2
2/3
15:
-1/685597979049984000*x^15 + 1/1171962357350400*x^14 - 4271/19588513687142400*x^13 + 163/5073430118400*x^12 - 22873897/7534043725824000*x^11 + 589403/3044058071040*x^10 - 8190557597/958878292377600*x^9 + 28011300229/106542032486400*x^8 - 240802807573/42807066624000*x^7 + 52255802219/634178764800*x^6 - 75622540254157/94175546572800*x^5 + 51972113464969/10463949619200*x^4 - 10741116809209327/595137134592000*x^3 + 517382600101/15414067200*x^2 - 555184667563/23616552960*x + 1
2
2/3
16:
1/23310331287699456000*x^16 - 83/2913791410962432000*x^15 + 883/105956051307724800*x^14 - 2111/1486628270899200*x^13 + 1827691/11643522121728000*x^12 - 190042453/16009842917376000*x^11 + 5143514981/8150465485209600*x^10 - 12160589009/509404092825600*x^9 + 104851282615231/163009309704192000*x^8 - 35628703913759/2910880530432000*x^7 + 206798022244867/1280787433390080*x^6 - 1145898447001699/800492145868800*x^5 + 119542830846462251/14716118237184000*x^4 - 551818757068018123/20234662576128000*x^3 + 962931965124341/20439053107200*x^2 - 24637308026197/802962800640*x + 1
2
3/4
0:
1
2
3/4
1:
-1/6*x + 1
2
3/4
2:
1/54*x^2 - 19/54*x + 1
2
3/4
3:
-1/648*x^3 + 13/216*x^2 - 181/324*x + 1
2
3/4
4:
1/9720*x^4 - 11/1620*x^3 + 1271/9720*x^2 - 427/540*x + 1
2
3/4
5:
-1/174960*x^5 + 5/8748*x^4 - 655/34992*x^3 + 2077/8748*x^2 - 15347/14580*x + 1
2
3/4
6:
1/3674160*x^6 - 47/1224720*x^5 + 1403/734832*x^4 - 3379/81648*x^3 + 89359/229635*x^2 - 413227/306180*x + 1
2
3/4
7:
-1/88179840*x^7 + 1/466560*x^6 - 1897/12597120*x^5 + 4175/839808*x^4 - 126389/1574640*x^3 + 626789/1049760*x^2 - 1033849/612360*x + 1
2
3/4
8:
1/2380855680*x^8 - 61/595213920*x^7 + 1643/170061120*x^6 - 9589/21257640*x^5 + 3782047/340122240*x^4 - 12133837/85030560*x^3 + 19294921/22044960*x^2 - 34333343/16533720*x + 1
2
3/4
9:
-1/71425670400*x^9 + 17/3968092800*x^8 - 6211/11904278400*x^7 + 3091/94478400*x^6 - 3885109/3401222400*x^5 + 471017/20995200*x^4 - 4258246781/17856417600*x^3 + 1231291027/992023200*x^2 - 25039109/9920232*x + 1
2
3/4
10:
1/2357047123200*x^10 - 5/31427294976*x^9 + 191/7856823744*x^8 - 51607/26189412480*x^7 + 10380193/112240339200*x^6 - 19276309/7482689280*x^5 + 1980126007/47140942464*x^4 - 14950030577/39284118720*x^3 + 56205219743/32736765600*x^2 - 1660030907/545612760*x + 1
2
3/4
11:
-1/84853696435200*x^11 + 41/7713972403200*x^10 - 1/1004423490*x^9 + 3721/36733201920*x^8 - 15811661/2571324134400*x^7 + 84650453/367332019200*x^6 - 4116235603/771397240320*x^5 + 28665058547/385698620160*x^4 - 62797187183/107138505600*x^3 + 2228810389/956593800*x^2 - 5968493491/1636838280*x + 1
2
3/4
12:
1/3309294160972800*x^12 - 89/551549026828800*x^11 + 10939/300844923724800*x^10 - 337/74282697216*x^9 + 34680271/100281641241600*x^8 - 280329799/16713606873600*x^7 + 157318391977/300844923724800*x^6 - 103846778173/10028164124160*x^5 + 9462121853699/75211230931200*x^4 - 3667789630517/4178401718400*x^3 + 8948592648637/2872651181400*x^2 - 277897718309/63836692920*x + 1
2
3/4
13:
-1/138990354760857600*x^13 + 1/222740953142400*x^12 - 12809/10691565750835200*x^11 + 607/3374862926400*x^10 - 5448727/323986840934400*x^9 + 6916031/6749725852800*x^8 - 40204182937/971960522803200*x^7 + 5587451929/5062294389600*x^6 - 2319027480709/121495065350400*x^5 + 693703239511/3374862926400*x^4 - 95429597619911/74246984380800*x^3 + 1414840715069/343736038800*x^2 - 110330250203/21278897640*x + 1
2
3/4
14:
1/6254565964238592000*x^14 - 103/893509423462656000*x^13 + 353/9818784873216000*x^12 - 439391/68731494112512000*x^11 + 1498361/2082772548864000*x^10 - 112009201/2082772548864000*x^9 + 119328447361/43738223526144000*x^8 - 589268457583/6248317646592000*x^7 + 958460566/435848050125*x^6 - 26356501714597/781039705824000*x^5 + 467172880962787/1431906127344000*x^4 - 881891277855509/477302042448000*x^3 + 1950195199998803/361954048856400*x^2 - 708770325997/114906047256*x + 1
2
3/4
15:
-1/300219166283452416000*x^15 + 1/363902019737518080*x^14 - 1699/1715538093048299520*x^13 + 15091/73313593720012800*x^12 - 90531337/3299111717400576000*x^11 + 9874433/3998923293818880*x^10 - 12910566649/83977389170196480*x^9 + 935023226623/139962315283660800*x^8 - 540633075049/2677850419968000*x^7 + 232158956759/55540601303040*x^6 - 475430528473361/8247779293501440*x^5 + 631804808780273/1249663529318400*x^4 - 681746107449513647/260606915176608000*x^3 + 12162260004057727/1737379434510720*x^2 - 25289470180973/3447181417680*x + 1
2
3/4
16:
1/15311177480456073216000*x^16 - 1/16358095598777856000*x^15 + 19301/765558874022803660800*x^14 - 55193/9113796119319091200*x^13 + 79397201/84127348793714688000*x^12 - 176353537/1752653099869056000*x^11 + 40378793801/5353558559600025600*x^10 - 738646337/1835925431961600*x^9 + 1637004074766031/107071171192000512000*x^8 - 261571483236197/637328399952384000*x^7 + 32139758308155983/4206367439685734400*x^6 - 16768008713385089/175265309986905600*x^5 + 27214173164220630787/35442540464018688000*x^4 - 1246343555511748693/340793658307872000*x^3 + 53406702388130855/5907090077336448*x^2 - 511597261570361/58602084100560*x + 1
3
1/4
0:
1
3
1/4
1:
-x + 1
3
1/4
2:
3/4*x^2 - 11/4*x + 1
3
1/4
3:
-9/20*x^3 + 18/5*x^2 - 123/20*x + 1
3
1/4
4:
9/40*x^4 - 63/20*x^3 + 99/8*x^2 - 269/20*x + 1
3
1/4
5:
-27/280*x^5 + 117/56*x^4 - 117/8*x^3 + 2139/56*x^2 - 4279/140*x + 1
3
1/4
6:
81/2240*x^6 - 2511/2240*x^5 + 783/64*x^4 - 25821/448*x^3 + 127917/1120*x^2 - 2949/40*x + 1
3
1/4
7:
-27/2240*x^7 + 81/160*x^6 - 1269/160*x^5 + 117/2*x^4 - 67329/320*x^3 + 54639/160*x^2 - 52963/280*x + 1
3
1/4
8:
81/22400*x^8 - 1107/5600*x^7 + 6723/1600*x^6 - 891/20*x^5 + 803727/3200*x^4 - 592479/800*x^3 + 5793927/5600*x^2 - 143543/280*x + 1
3
1/4
9:
-243/246400*x^9 + 16767/246400*x^8 - 46413/24640*x^7 + 477009/17600*x^6 - 7729101/35200*x^5 + 35679609/35200*x^4 - 3950343/1540*x^3 + 196555761/61600*x^2 - 4478373/3080*x + 1
3
1/4
10:
243/985600*x^10 - 4131/197120*x^9 + 6561/8960*x^8 - 1351971/98560*x^7 + 21218517/140800*x^6 - 28105461/28160*x^5 + 194276367/49280*x^4 - 435464937/49280*x^3 + 308707659/30800*x^2 - 13177343/3080*x + 1
3
1/4
11:
-729/12812800*x^11 + 243/41600*x^10 - 58563/232960*x^9 + 21627/3640*x^8 - 98897517/1164800*x^7 + 31670919/41600*x^6 - 1002465801/232960*x^5 + 62370027/4160*x^4 - 8865908811/291200*x^3 + 1165973727/36400*x^2 - 519273499/40040*x + 1
3
1/4
12:
2187/179379200*x^12 - 133407/89689600*x^11 + 13851/179200*x^10 - 3667113/1630720*x^9 + 660560751/16307200*x^8 - 549527733/1164800*x^7 + 58747019283/16307200*x^6 - 5839079319/326144*x^5 + 32758311519/582400*x^4 - 214492598433/2038400*x^3 + 72861082731/700700*x^2 - 1612895919/40040*x + 1
3
1/4
13:
-2187/896896000*x^13 + 2187/6272000*x^12 - 212139/9856000*x^11 + 947943/1254400*x^10 - 105004917/6272000*x^9 + 31420629/128000*x^8 - 15242702229/6272000*x^7 + 4083081129/250880*x^6 - 32557715991/448000*x^5 + 328191920523/1568000*x^4 - 3150503479251/8624000*x^3 + 68456601/200*x^2 - 5112495671/40040*x + 1
3
1/4
14:
6561/14350336000*x^14 - 155277/2050048000*x^13 + 172773/31539200*x^12 - 36007497/157696000*x^11 + 87443793/14336000*x^10 - 1575106317/14336000*x^9 + 27442085499/20070400*x^8 - 169838153001/14336000*x^7 + 509551543233/7168000*x^6 - 1039077476811/3584000*x^5 + 611265079107/788480*x^4 - 196318538883/154000*x^3 + 25577186859507/22422400*x^2 - 942068707/2288*x + 1
3
1/4
15:
-19683/243955712000*x^15 + 373977/24395571200*x^14 - 203391/158412800*x^13 + 8400267/134041600*x^12 - 2662057953/1340416000*x^11 + 32818851/761600*x^10 - 28060655121/42649600*x^9 + 35892562131/5017600*x^8 - 13504428543159/243712000*x^7 + 1475951908419/4874240*x^6 - 153124910268327/134041600*x^5 + 191979595250631/67020800*x^4 - 774840336399639/173264000*x^3 + 1465042299456339/381180800*x^2 - 262055181639/194480*x + 1
3
1/4
16:
6561/487911424000*x^16 - 177147/60988928000*x^15 + 400221/1435033600*x^14 - 13727799/871270400*x^13 + 142402131/243712000*x^12 - 22480173/1496000*x^11 + 47094664329/170598400*x^10 - 156824164233/42649600*x^9 + 121723234563951/3411968000*x^8 - 15298656896781/60928000*x^7 + 1995800485527/1576960*x^6 - 5339251346463/1196800*x^5 + 322446162055339449/30494464000*x^4 - 60112260987752763/3811808000*x^3 + 453158854691589/34652800*x^2 - 868653019199/194480*x + 1
3
1/3
0:
1
3
1/3
1:
-2/3*x + 1
3
1/3
2:
1/3*x^2 - 5/3*x + 1
3
1/3
3:
-2/15*x^3 + 7/5*x^2 - 49/15*x + 1
3
1/3
4:
2/45*x^4 - 4/5*x^3 + 184/45*x^2 - 6*x + 1
3
1/3
5:
-4/315*x^5 + 22/63*x^4 - 28/9*x^3 + 656/63*x^2 - 384/35*x + 1
3
1/3
6:
1/315*x^6 - 13/105*x^5 + 107/63*x^4 - 211/21*x^3 + 7879/315*x^2 - 719/35*x + 1
3
1/3
7:
-2/2835*x^7 + 1/27*x^6 - 293/405*x^5 + 179/27*x^4 - 11939/405*x^3 + 529/9*x^2 - 12571/315*x + 1
3
1/3
8:
2/14175*x^8 - 136/14175*x^7 + 512/2025*x^6 - 268/81*x^5 + 46334/2025*x^4 - 166132/2025*x^3 + 216824/1575*x^2 - 25444/315*x + 1
3
1/3
9:
-4/155925*x^9 + 38/17325*x^8 - 3896/51975*x^7 + 656/495*x^6 - 97336/7425*x^5 + 181306/2475*x^4 - 34576412/155925*x^3 + 1124296/3465*x^2 - 589466/3465*x + 1
3
1/3
10:
2/467775*x^10 - 2/4455*x^9 + 86/4455*x^8 - 4604/10395*x^7 + 131936/22275*x^6 - 7816/165*x^5 + 20914664/93555*x^4 - 2629234/4455*x^3 + 521869/675*x^2 - 1286603/3465*x + 1
3
1/3
11:
-4/6081075*x^11 + 46/552825*x^10 - 2/455*x^9 + 4678/36855*x^8 - 406004/184275*x^7 + 627088/26325*x^6 - 17781656/110565*x^5 + 73105216/110565*x^4 - 287346208/184275*x^3 + 114597559/61425*x^2 - 37646879/45045*x + 1
3
1/3
12:
4/42567525*x^12 - 8/567567*x^11 + 496/552825*x^10 - 8212/257985*x^9 + 68998/99225*x^8 - 119848/12285*x^7 + 344348416/3869775*x^6 - 134852176/257985*x^5 + 151280036/78975*x^4 - 1060395272/257985*x^3 + 21568722848/4729725*x^2 - 86967194/45045*x + 1
3
1/3
13:
-8/638512875*x^13 + 4/1819125*x^12 - 8152/49116375*x^11 + 704/99225*x^10 - 283376/1488375*x^9 + 555722/165375*x^8 - 177470456/4465125*x^7 + 2084192/6615*x^6 - 7352497816/4465125*x^5 + 2715795692/496125*x^4 - 59161471448/5457375*x^3 + 1368553064/121275*x^2 - 205341956/45045*x + 1
3
1/3
14:
1/638512875*x^14 - 29/91216125*x^13 + 197/7016625*x^12 - 1997/1403325*x^11 + 9781/212625*x^10 - 211973/212625*x^9 + 66193537/4465125*x^8 - 19420873/127575*x^7 + 683794151/637875*x^6 - 3234343603/637875*x^5 + 4028808451/259875*x^4 - 178730329/6237*x^3 + 44530998791/1576575*x^2 - 493886069/45045*x + 1
3
1/3
15:
-2/10854718875*x^15 + 31/723647925*x^14 - 1357/310134825*x^13 + 2063/7952175*x^12 - 1185749/119282625*x^11 + 20837/80325*x^10 - 71863249/15181425*x^9 + 18175259/297675*x^8 - 6031923101/10843875*x^7 + 2558104301/722925*x^6 - 366275959769/23856525*x^5 + 115707832481/2650725*x^4 - 91656018530707/1206079875*x^3 + 127644732037/1786785*x^2 - 20515006009/765765*x + 1
3
1/3
16:
2/97692469875*x^16 - 16/2960377875*x^15 + 12352/19538493975*x^14 - 40328/930404475*x^13 + 2085164/1073543625*x^12 - 7163864/119282625*x^11 + 180203152/136632825*x^10 - 950031976/45544275*x^9 + 162897201722/683164125*x^8 - 63744907528/32531625*x^7 + 2450012602592/214708725*x^6 - 99569324072/2168775*x^5 + 1329340277090092/10854718875*x^4 - 243964476334312/1206079875*x^3 + 8799410812048/48243195*x^2 - 5645827576/85085*x + 1
3
1/2
0:
1
3
1/2
1:
-1/3*x + 1
3
1/2
2:
1/12*x^2 - 3/4*x + 1
3
1/2
3:
-1/60*x^3 + 3/10*x^2 - 77/60*x + 1
3
1/2
4:
1/360*x^4 - 1/12*x^3 + 263/360*x^2 - 119/60*x + 1
3
1/2
5:
-1/2520*x^5 + 1/56*x^4 - 19/72*x^3 + 253/168*x^2 - 1229/420*x + 1
3
1/2
6:
1/20160*x^6 - 1/320*x^5 + 281/4032*x^4 - 911/1344*x^3 + 4091/1440*x^2 - 3553/840*x + 1
3
1/2
7:
-1/181440*x^7 + 1/2160*x^6 - 47/3240*x^5 + 185/864*x^4 - 40057/25920*x^3 + 7331/1440*x^2 - 15319/2520*x + 1
3
1/2
8:
1/1814400*x^8 - 1/16800*x^7 + 323/129600*x^6 - 7/135*x^5 + 147967/259200*x^4 - 70613/21600*x^3 + 148661/16800*x^2 - 491/56*x + 1
3
1/2
9:
-1/19958400*x^9 + 1/147840*x^8 - 1213/3326400*x^7 + 1609/158400*x^6 - 150229/950400*x^5 + 87877/63360*x^4 - 16417729/2494800*x^3 + 8378081/554400*x^2 - 353981/27720*x + 1
3
1/2
10:
1/239500800*x^10 - 1/1451520*x^9 + 53/1140480*x^8 - 4441/2661120*x^7 + 397213/11404800*x^6 - 109733/253440*x^5 + 37834861/11975040*x^4 - 51123841/3991680*x^3 + 3037811/118800*x^2 - 104539/5544*x + 1
3
1/2
11:
-1/3113510400*x^11 + 1/15724800*x^10 - 11/2096640*x^9 + 53/224640*x^8 - 599531/94348800*x^7 + 238319/2246400*x^6 - 62210303/56609280*x^5 + 2701381/393120*x^4 - 574449943/23587200*x^3 + 2017631/46800*x^2 - 2039407/72072*x + 1
3
1/2
12:
1/43589145600*x^12 - 1/186278400*x^11 + 43/80870400*x^10 - 773/26417664*x^9 + 1304431/1320883200*x^8 - 669727/31449600*x^7 + 1175188201/3962649600*x^6 - 7738303/2935296*x^5 + 2044252397/141523200*x^4 - 7525492321/165110400*x^3 + 1375354103/18918900*x^2 - 3113755/72072*x + 1
3
1/2
13:
-1/653837184000*x^13 + 1/2395008000*x^12 - 2459/50295168000*x^11 + 197/60963840*x^10 - 4153/31104000*x^9 + 611299/169344000*x^8 - 297069187/4572288000*x^7 + 33838517/43545600*x^6 - 13851823501/2286144000*x^5 + 11278316293/381024000*x^4 - 8420830421/99792000*x^3 + 357755023/2910600*x^2 - 3455369/51480*x + 1
3
1/2
14:
1/10461394944000*x^14 - 1/33210777600*x^13 + 43/10450944000*x^12 - 12323/38320128000*x^11 + 6179/387072000*x^10 - 122753/232243200*x^9 + 872883463/73156608000*x^8 - 71420011/387072000*x^7 + 10119704353/5225472000*x^6 - 469281761/34836480*x^5 + 285013047097/4790016000*x^4 - 967511827/6237000*x^3 + 11486865947/55036800*x^2 - 76431337/720720*x + 1
3
1/2
15:
-1/177843714048000*x^15 + 1/494010316800*x^14 - 811/2540624486400*x^13 + 271/9306316800*x^12 - 208837/122145408000*x^11 + 402859/5922201600*x^10 - 233940727/124366233600*x^9 + 29662657/812851200*x^8 - 88002294103/177666048000*x^7 + 3924586123/846028800*x^6 - 2851264357471/97716326400*x^5 + 1919733773473/16286054400*x^4 - 43830431873587/154378224000*x^3 + 3666635712893/10291881600*x^2 - 2085626237/12252240*x + 1
3
1/2
16:
1/3201186852864000*x^16 - 1/7846046208000*x^15 + 3677/160059342643200*x^14 - 419/173224396800*x^13 + 2915921/17588938752000*x^12 - 476521/61072704000*x^11 + 290231609/1119296102400*x^10 - 574813103/93274675200*x^9 + 2349271022671/22385922048000*x^8 - 9962793263/7838208000*x^7 + 378640313627/35177877504*x^6 - 378086915317/6107270400*x^5 + 5133898471135121/22230464256000*x^4 - 14549744276449/28068768000*x^3 + 18884853715879/30875644800*x^2 - 3396796097/12252240*x + 1
3
2/3
0:
1
3
2/3
1:
-1/6*x + 1
3
2/3
2:
1/48*x^2 - 17/48*x + 1
3
2/3
3:
-1/480*x^3 + 11/160*x^2 - 17/30*x + 1
3
2/3
4:
1/5760*x^4 - 3/320*x^3 + 175/1152*x^2 - 259/320*x + 1
3
2/3
5:
-1/80640*x^5 + 1/1008*x^4 - 61/2304*x^3 + 1133/4032*x^2 - 2439/2240*x + 1
3
2/3
6:
1/1290240*x^6 - 37/430080*x^5 + 881/258048*x^4 - 5167/86016*x^3 + 303257/645120*x^2 - 25327/17920*x + 1
3
2/3
7:
-1/23224320*x^7 + 7/1105920*x^6 - 1159/3317760*x^5 + 2029/221184*x^4 - 198701/1658880*x^3 + 4249/5760*x^2 - 144619/80640*x + 1
3
2/3
8:
1/464486400*x^8 - 47/116121600*x^7 + 983/33177600*x^6 - 1799/1658880*x^5 + 1407367/66355200*x^4 - 3638909/16588800*x^3 + 14299963/12902400*x^2 - 1446647/645120*x + 1
3
2/3
9:
-1/10218700800*x^9 + 13/567705600*x^8 - 731/340623360*x^7 + 4231/40550400*x^6 - 1387069/486604800*x^5 + 3593651/81100800*x^4 - 193322137/510935040*x^3 + 229152499/141926400*x^2 - 19712017/7096320*x + 1
3
2/3
10:
1/245248819200*x^10 - 19/16349921280*x^9 + 1109/8174960640*x^8 - 23033/2724986880*x^7 + 3587173/11678515200*x^6 - 1734541/259522560*x^5 + 263842651/3065610240*x^4 - 232068523/371589120*x^3 + 3916964389/1703116800*x^2 - 48562919/14192640*x + 1
3
2/3
11:
-1/6376469299200*x^11 + 31/579679027200*x^10 - 7/920125440*x^9 + 1631/2760376320*x^8 - 5322041/193226342400*x^7 + 22034563/27603763200*x^6 - 208924633/14491975680*x^5 + 4587110377/28983951360*x^4 - 1720091101/1725235200*x^3 + 231627689/71884800*x^2 - 387748771/92252160*x + 1
3
2/3
12:
1/178541140377600*x^12 - 67/29756856729600*x^11 + 127/331245158400*x^10 - 1511/41617981440*x^9 + 11421391/5410337587200*x^8 - 10118791/128817561600*x^7 + 30707471149/16231012761600*x^6 - 3157768633/108206751744*x^5 + 161708825987/579679027200*x^4 - 1048997721923/676292198400*x^3 + 2764503003091/619934515200*x^2 - 3808051733/738017280*x + 1
3
2/3
13:
-1/5356234211328000*x^13 + 1/11444944896000*x^12 - 7229/412018016256000*x^11 + 23/11560550400*x^10 - 1761847/12485394432000*x^9 + 2272901/346816512000*x^8 - 7597037317/37456183296000*x^7 + 43460059/10404495360*x^6 - 65783450461/1170505728000*x^5 + 41228224813/86704128000*x^4 - 6765810261061/2861236224000*x^3 + 97217010959/15895756800*x^2 - 4679926187/738017280*x + 1
3
2/3
14:
1/171399494762496000*x^14 - 1/317995352064000*x^13 + 277/376702186291200*x^12 - 185257/1883510931456000*x^11 + 476971/57076088832000*x^10 - 3861977/8153726976000*x^9 + 4388373323/239719573094400*x^8 - 83014110281/171228266496000*x^7 + 746413506553/85614133248000*x^6 - 4451454143611/42807066624000*x^5 + 1375896990389/1743991603200*x^4 - 4707603293/1327104000*x^3 + 27551570703667/3306317414400*x^2 - 18449875897/2361655296*x + 1
3
2/3
15:
-1/5827582821924864000*x^15 + 41/388505521461657600*x^14 - 4733/166502366340710400*x^13 + 2701/609898777804800*x^12 - 28431607/64039371669504000*x^11 + 1300319/43124156006400*x^10 - 11596821311/8150465485209600*x^9 + 7524566701/159813048729600*x^8 - 3171634114799/2910880530432000*x^7 + 48200512757/2772267171840*x^6 - 298143067247477/1600984291737600*x^5 + 56943739016237/44471785881600*x^4 - 26574481420753807/5058665644032000*x^3 + 105871782666389/9367899340800*x^2 - 969462679919/100370350080*x + 1
3
2/3
16:
1/209792981589295104000*x^16 - 29/8741374232887296000*x^15 + 10697/10489649079464755200*x^14 - 1039/5676217034342400*x^13 + 24642281/1152708690051072000*x^12 - 27433963/16009842917376000*x^11 + 7109597309/73354189366886400*x^10 - 11972666443/3056424556953600*x^9 + 166251746895391/1467083787337728000*x^8 - 20333925610717/8732641591296000*x^7 + 384947117394739/11527086900510720*x^6 - 259830079554623/800492145868800*x^5 + 2973172819463906201/1456895705481216000*x^4 - 14163658207395353/1839514779648000*x^3 + 30919633888314439/2023466257612800*x^2 - 3210478501519/267654266880*x + 1
3
3/4
0:
1
3
3/4
1:
-1/9*x + 1
3
3/4
2:
1/108*x^2 - 25/108*x + 1
3
3/4
3:
-1/1620*x^3 + 4/135*x^2 - 587/1620*x + 1
3
3/4
4:
1/29160*x^4 - 13/4860*x^3 + 1847/29160*x^2 - 491/972*x + 1
3
3/4
5:
-1/612360*x^5 + 23/122472*x^4 - 127/17496*x^3 + 13849/122472*x^2 - 67519/102060*x + 1
3
3/4
6:
1/14696640*x^6 - 53/4898880*x^5 + 1817/2939328*x^4 - 191/12096*x^3 + 1338077/7348320*x^2 - 510449/612360*x + 1
3
3/4
7:
-1/396809280*x^7 + 1/1889568*x^6 - 1187/28343520*x^5 + 749/472392*x^4 - 1707307/56687040*x^3 + 172777/629856*x^2 - 5640841/5511240*x + 1
3
3/4
8:
1/11904278400*x^8 - 67/2976069600*x^7 + 2003/850305600*x^6 - 263/2125764*x^5 + 5939167/1700611200*x^4 - 22377679/425152800*x^3 + 14494567/36741600*x^2 - 20404687/16533720*x + 1
3
3/4
9:
-1/392841187200*x^9 + 37/43649020800*x^8 - 7417/65473531200*x^7 + 1637/207852480*x^6 - 5778709/18706723200*x^5 + 14417473/2078524800*x^4 - 530476757/6138143550*x^3 + 1196952367/2182451040*x^2 - 801317639/545612760*x + 1
3
3/4
10:
1/14142282739200*x^10 - 1/34919216640*x^9 + 2243/471409424640*x^8 - 22147/52378824960*x^7 + 1345463/61222003200*x^6 - 10277909/14965378560*x^5 + 9037668613/707114136960*x^4 - 3547254089/26189412480*x^3 + 36494161817/49105148400*x^2 - 944436517/545612760*x + 1
3
3/4
11:
-1/551549026828800*x^11 + 11/12535205155200*x^10 - 593/3342721374720*x^9 + 4097/208920085920*x^8 - 21791351/16713606873600*x^7 + 32262683/596914531200*x^6 - 14060045609/10028164124160*x^5 + 27889032193/1253520515520*x^4 - 285220808371/1392800572800*x^3 + 171889176343/174100071600*x^2 - 43103392043/21278897640*x + 1
3
3/4
12:
1/23165059126809600*x^12 - 19/772168637560320*x^11 + 1789/300844923724800*x^10 - 6241/7799683207680*x^9 + 46479631/701971488691200*x^8 - 1677869/477531624960*x^7 + 254880745369/2105914466073600*x^6 - 188207051827/70197148869120*x^5 + 2786024777597/75211230931200*x^4 - 1760352836239/5849762405760*x^3 + 998677734869/773406087300*x^2 - 150536967869/63836692920*x + 1
3
3/4
13:
-1/1042427660706432000*x^13 + 17/26728914377088000*x^12 - 14519/80186743131264000*x^11 + 14159/485980261401600*x^10 - 7133797/2429901307008000*x^9 + 52378709/269989034112000*x^8 - 62402389807/7289703921024000*x^7 + 24499106753/97196052280320*x^6 - 17745427255051/3644851960512000*x^5 + 36151051191443/607475326752000*x^4 - 481317413219257/1113704765712000*x^3 + 7739837508443/4640436523800*x^2 - 523792416703/191510078760*x + 1
3
3/4
14:
1/50036527713908736000*x^14 - 109/7148075387701248000*x^13 + 2777/549851952900096000*x^12 - 15043/15710055797145600*x^11 + 274733/2380311484416000*x^10 - 154811983/16662180390912000*x^9 + 178725903367/349905788209152000*x^8 - 38547311857/1999461646909440*x^7 + 12382544356513/24993270586368000*x^6 - 15135612170621/1785233613312000*x^5 + 303904350177599/3272928291072000*x^4 - 7268260992229/11932551061200*x^3 + 6176146479608681/2895632390851200*x^2 - 3635873095187/1149060472560*x + 1
3
3/4
15:
-1/2551862913409345536000*x^15 + 29/85062097113644851200*x^14 - 2369/18227592238638182400*x^13 + 1489/51930462218342400*x^12 - 57112031/14021224798952448000*x^11 + 8335043/21244279998412800*x^10 - 5863268627/223064939983334400*x^9 + 21635307893/17495289410457600*x^8 - 103916630244613/2549313599809536000*x^7 + 26312081762053/28325706664550400*x^6 - 19997589803707573/1402122479895244800*x^5 + 33045679854354743/233687079982540800*x^4 - 1872287257976623847/2215158779001168000*x^3 + 79909838324593583/29535450386682240*x^2 - 214193229645361/58602084100560*x + 1
3
3/4
16:
1/137800597324104658944000*x^16 - 41/5741691555171027456000*x^15 + 21389/6890029866205232947200*x^14 - 5879/7456742279442892800*x^13 + 98694641/757146139143432192000*x^12 - 347419/23473032587532000*x^11 + 57182240489/48182027036400230400*x^10 - 273303357923/4015168919700019200*x^9 + 2696268749207311/963640540728004608000*x^8 - 469404743725423/5735955599571456000*x^7 + 63398511441474947/37857306957171609600*x^6 - 875371393264111/37556852140051200*x^5 + 201928794162513156881/956948592528504576000*x^4 - 466253155043219339/402756141636576000*x^3 + 906312218537402939/265819053480140160*x^2 - 2225143098733249/527418756905040*x + 1
Definition
For rational $\beta>0$, rational $0<c<1$ and integer $n\geq0$, the Meixner polynomial $M_n(x;\beta,c)$ is the degree-$n$ polynomial defined by the terminating hypergeometric sum (1), in the normalisation of DLMF [2].
Parameters
$\beta$
—   shape parameter ($\beta>0$)
$c$
—   weight parameter ($0<c<1$)
$n$
—   degree ($n\geq0$)
Formulas
(1)
$M_n(x;\beta,c)={}_2F_1\left(\begin{matrix}-n,-x\\\beta\end{matrix};1-c^{-1}\right)=\sum_{k=0}^{n}\frac{(-n)_k(-x)_k}{(\beta)_k k!}(1-c^{-1})^k$ [2].
(2)
$(1-t/c)^x(1-t)^{-x-\beta}=\sum_{n=0}^{\infty}(\beta)_n M_n(x;\beta,c)t^n/n!$ [5].
(3)
$M_0(x;\beta,c)=1$, $M_1(x;\beta,c)=1+(1-c^{-1})x/\beta$, and $(c-1)xM_n=c(n+\beta)M_{n+1}-(n+(n+\beta)c)M_n+nM_{n-1}$ for $n\geq1$ [4].
(4)
$M_n(0;\beta,c)=1$ for every $n\geq0$.
(5)
For $m\ne n$, $\sum_{x=0}^{\infty}(\beta)_x c^x M_m(x;\beta,c)M_n(x;\beta,c)/x! = 0$, and the same sum with $m=n$ is $c^{-n}n!/((\beta)_n(1-c)^\beta)$ [1].
Comments
(6)
These are also called the discrete Laguerre polynomials. The variable $x$ runs over the non-negative integers for the negative-binomial weight $(\beta)_x c^x/x!$; the entries are polynomials in that variable.
(7)
The polynomial in the normalisation used by the Wikipedia article [8] is $(\beta)_n M_n(x;\beta,c)$.
Links
Similar tables
Hahn polynomials —   satisfy $\lim_{N\to\infty}Q_n(x;\beta-1,N(c^{-1}-1),N)=M_n(x;\beta,c)$ [6]
Charlier polynomials —   are the limit of $M_n(x;\beta,a/(a+\beta))$ as $\beta\to\infty$ [7]
Krawtchouk polynomials of the Hamming scheme —   satisfy $\mathcal{K}_k(x;N,q)=\binom{N}{k}(q-1)^k M_k(x;-N,1-q)$, a Meixner specialisation outside the parameter range $\beta>0$, $0<c<1$ [3] [2]
Laguerre polynomials —   satisfy $L_n(x)=\lim_{c\to1}M_n(x/(1-c);1,c)$ [9]
Data properties
Entries are of type: rational polynomial
Table is complete: no (it holds $\beta\in\{\tfrac12,1,\tfrac32,2,3\}$, $c\in\{\tfrac14,\tfrac13,\tfrac12,\tfrac23,\tfrac34\}$ and every degree $0\leq n\leq16$)
How they were obtained:

The generator computes the terminating hypergeometric sum in Sage's rational polynomial ring $\mathbb{Q}[x]$, with every division made in $\mathbb{Q}$.

more

The entries were checked against the three-term recurrence, the generating function, exact orthogonality after multiplying by $(1-c)^\beta$ and evaluating the negative-binomial moments in the falling-factorial basis, the value $M_n(0;\beta,c)=1$, DLMF's Meixner-Charlier and Hahn-Meixner limits, the Hamming Krawtchouk specialisation, and the rescaling used by the Wikipedia article.