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Where each entry of Gegenbauer polynomials came from

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339 entries, page 2 of 2. previous

alphan value last changed by
3/4 9 15646785/65536*x^9 - 4023459/8192*x^7 + 2725569/8192*x^5 - 168245/204… 2026-08-09 — flattening
3/4 10 122044923/262144*x^10 - 140821065/131072*x^8 + 28164213/32768*x^6 - 4… 2026-08-09 — flattening
3/4 11 477084699/524288*x^11 - 610224615/262144*x^9 + 140821065/65536*x^7 - … 2026-08-09 — flattening
3/4 12 7474326951/4194304*x^12 - 5247931689/1048576*x^10 + 5492021535/104857… 2026-08-09 — flattening
3/4 13 29322359577/8388608*x^13 - 22422980853/2097152*x^11 + 26239658445/209… 2026-08-09 — flattening
3/4 14 230389968105/33554432*x^14 - 381190674501/16777216*x^12 + 24665278938… 2026-08-09 — flattening
3/4 15 906200541213/67108864*x^15 - 1612729776735/33554432*x^13 + 1143572023… 2026-08-09 — flattening
3/4 16 57090634096419/2147483648*x^16 - 13593008118195/134217728*x^14 + 2096… 2026-08-09 — flattening
3/4 17 225004263791769/4294967296*x^17 - 57090634096419/268435456*x^15 + 951… 2026-08-09 — flattening
3/4 18 1775033636579511/17179869184*x^18 - 3825072484460073/8589934592*x^16 … 2026-08-09 — flattening
3/4 19 7006711723340175/34359738368*x^19 - 15975302729215599/17179869184*x^1… 2026-08-09 — flattening
3/4 20 110706045228774765/274877906944*x^20 - 133127522743463325/68719476736… 2026-08-09 — flattening
1 None —
3/2 0 1 2026-08-09 — flattening
3/2 1 3*x 2026-08-09 — flattening
3/2 2 15/2*x^2 - 3/2 2026-08-09 — flattening
3/2 3 35/2*x^3 - 15/2*x 2026-08-09 — flattening
3/2 4 315/8*x^4 - 105/4*x^2 + 15/8 2026-08-09 — flattening
3/2 5 693/8*x^5 - 315/4*x^3 + 105/8*x 2026-08-09 — flattening
3/2 6 3003/16*x^6 - 3465/16*x^4 + 945/16*x^2 - 35/16 2026-08-09 — flattening
3/2 7 6435/16*x^7 - 9009/16*x^5 + 3465/16*x^3 - 315/16*x 2026-08-09 — flattening
3/2 8 109395/128*x^8 - 45045/32*x^6 + 45045/64*x^4 - 3465/32*x^2 + 315/128 2026-08-09 — flattening
3/2 9 230945/128*x^9 - 109395/32*x^7 + 135135/64*x^5 - 15015/32*x^3 + 3465/… 2026-08-09 — flattening
3/2 10 969969/256*x^10 - 2078505/256*x^8 + 765765/128*x^6 - 225225/128*x^4 +… 2026-08-09 — flattening
3/2 11 2028117/256*x^11 - 4849845/256*x^9 + 2078505/128*x^7 - 765765/128*x^5… 2026-08-09 — flattening
3/2 12 16900975/1024*x^12 - 22309287/512*x^10 + 43648605/1024*x^8 - 4849845/… 2026-08-09 — flattening
3/2 13 35102025/1024*x^13 - 50702925/512*x^11 + 111546435/1024*x^9 - 1454953… 2026-08-09 — flattening
3/2 14 145422675/2048*x^14 - 456326325/2048*x^12 + 557732175/2048*x^10 - 334… 2026-08-09 — flattening
3/2 15 300540195/2048*x^15 - 1017958725/2048*x^13 + 1368978975/2048*x^11 - 9… 2026-08-09 — flattening
3/2 16 9917826435/32768*x^16 - 4508102925/4096*x^14 + 13233463425/8192*x^12 … 2026-08-09 — flattening
3/2 17 20419054425/32768*x^17 - 9917826435/4096*x^15 + 31556720475/8192*x^13… 2026-08-09 — flattening
3/2 18 83945001525/65536*x^18 - 347123925225/65536*x^16 + 148767396525/16384… 2026-08-09 — flattening
3/2 19 172308161025/65536*x^19 - 755505013725/65536*x^17 + 347123925225/1638… 2026-08-09 — flattening
3/2 20 1412926920405/262144*x^20 - 3273855059475/131072*x^18 + 1284358523332… 2026-08-09 — flattening
2 0 1 2026-08-09 — flattening
2 1 4*x 2026-08-09 — flattening
2 2 12*x^2 - 2 2026-08-09 — flattening
2 3 32*x^3 - 12*x 2026-08-09 — flattening
2 4 80*x^4 - 48*x^2 + 3 2026-08-09 — flattening
2 5 192*x^5 - 160*x^3 + 24*x 2026-08-09 — flattening
2 6 448*x^6 - 480*x^4 + 120*x^2 - 4 2026-08-09 — flattening
2 7 1024*x^7 - 1344*x^5 + 480*x^3 - 40*x 2026-08-09 — flattening
2 8 2304*x^8 - 3584*x^6 + 1680*x^4 - 240*x^2 + 5 2026-08-09 — flattening
2 9 5120*x^9 - 9216*x^7 + 5376*x^5 - 1120*x^3 + 60*x 2026-08-09 — flattening
2 10 11264*x^10 - 23040*x^8 + 16128*x^6 - 4480*x^4 + 420*x^2 - 6 2026-08-09 — flattening
2 11 24576*x^11 - 56320*x^9 + 46080*x^7 - 16128*x^5 + 2240*x^3 - 84*x 2026-08-09 — flattening
2 12 53248*x^12 - 135168*x^10 + 126720*x^8 - 53760*x^6 + 10080*x^4 - 672*x… 2026-08-09 — flattening
2 13 114688*x^13 - 319488*x^11 + 337920*x^9 - 168960*x^7 + 40320*x^5 - 403… 2026-08-09 — flattening
2 14 245760*x^14 - 745472*x^12 + 878592*x^10 - 506880*x^8 + 147840*x^6 - 2… 2026-08-09 — flattening
2 15 524288*x^15 - 1720320*x^13 + 2236416*x^11 - 1464320*x^9 + 506880*x^7 … 2026-08-09 — flattening
2 16 1114112*x^16 - 3932160*x^14 + 5591040*x^12 - 4100096*x^10 + 1647360*x… 2026-08-09 — flattening
2 17 2359296*x^17 - 8912896*x^15 + 13762560*x^13 - 11182080*x^11 + 5125120… 2026-08-09 — flattening
2 18 4980736*x^18 - 20054016*x^16 + 33423360*x^14 - 29818880*x^12 + 153753… 2026-08-09 — flattening
2 19 10485760*x^19 - 44826624*x^17 + 80216064*x^15 - 77987840*x^13 + 44728… 2026-08-09 — flattening
2 20 22020096*x^20 - 99614720*x^18 + 190513152*x^16 - 200540160*x^14 + 126… 2026-08-09 — flattening
5/2 0 1 2026-08-09 — flattening
5/2 1 5*x 2026-08-09 — flattening
5/2 2 35/2*x^2 - 5/2 2026-08-09 — flattening
5/2 3 105/2*x^3 - 35/2*x 2026-08-09 — flattening
5/2 4 1155/8*x^4 - 315/4*x^2 + 35/8 2026-08-09 — flattening
5/2 5 3003/8*x^5 - 1155/4*x^3 + 315/8*x 2026-08-09 — flattening
5/2 6 15015/16*x^6 - 15015/16*x^4 + 3465/16*x^2 - 105/16 2026-08-09 — flattening
5/2 7 36465/16*x^7 - 45045/16*x^5 + 15015/16*x^3 - 1155/16*x 2026-08-09 — flattening
5/2 8 692835/128*x^8 - 255255/32*x^6 + 225225/64*x^4 - 15015/32*x^2 + 1155/… 2026-08-09 — flattening
5/2 9 1616615/128*x^9 - 692835/32*x^7 + 765765/64*x^5 - 75075/32*x^3 + 1501… 2026-08-09 — flattening
5/2 10 7436429/256*x^10 - 14549535/256*x^8 + 4849845/128*x^6 - 1276275/128*x… 2026-08-09 — flattening
5/2 11 16900975/256*x^11 - 37182145/256*x^9 + 14549535/128*x^7 - 4849845/128… 2026-08-09 — flattening
5/2 12 152108775/1024*x^12 - 185910725/512*x^10 + 334639305/1024*x^8 - 33948… 2026-08-09 — flattening
5/2 13 339319575/1024*x^13 - 456326325/512*x^11 + 929553625/1024*x^9 - 11154… 2026-08-09 — flattening
5/2 14 1502700975/2048*x^14 - 4411154475/2048*x^12 + 5019589575/2048*x^10 - … 2026-08-09 — flattening
5/2 15 3305942145/2048*x^15 - 10518906825/2048*x^13 + 13233463425/2048*x^11 … 2026-08-09 — flattening
5/2 16 115707975075/32768*x^16 - 49589132175/4096*x^14 + 136745788725/8192*x… 2026-08-09 — flattening
5/2 17 251835004575/32768*x^17 - 115707975075/4096*x^15 + 347123925225/8192*… 2026-08-09 — flattening
5/2 18 1091285019825/65536*x^18 - 4281195077775/65536*x^16 + 1735619626125/1… 2026-08-09 — flattening
5/2 19 2354878200675/65536*x^19 - 9821565178425/65536*x^17 + 4281195077775/1… 2026-08-09 — flattening
5/2 20 20251952525805/262144*x^20 - 44742685812825/131072*x^18 + 16696660803… 2026-08-09 — flattening
3 0 1 2026-08-09 — flattening
3 1 6*x 2026-08-09 — flattening
3 2 24*x^2 - 3 2026-08-09 — flattening
3 3 80*x^3 - 24*x 2026-08-09 — flattening
3 4 240*x^4 - 120*x^2 + 6 2026-08-09 — flattening
3 5 672*x^5 - 480*x^3 + 60*x 2026-08-09 — flattening
3 6 1792*x^6 - 1680*x^4 + 360*x^2 - 10 2026-08-09 — flattening
3 7 4608*x^7 - 5376*x^5 + 1680*x^3 - 120*x 2026-08-09 — flattening
3 8 11520*x^8 - 16128*x^6 + 6720*x^4 - 840*x^2 + 15 2026-08-09 — flattening
3 9 28160*x^9 - 46080*x^7 + 24192*x^5 - 4480*x^3 + 210*x 2026-08-09 — flattening
3 10 67584*x^10 - 126720*x^8 + 80640*x^6 - 20160*x^4 + 1680*x^2 - 21 2026-08-09 — flattening
3 11 159744*x^11 - 337920*x^9 + 253440*x^7 - 80640*x^5 + 10080*x^3 - 336*x 2026-08-09 — flattening
3 12 372736*x^12 - 878592*x^10 + 760320*x^8 - 295680*x^6 + 50400*x^4 - 302… 2026-08-09 — flattening
3 13 860160*x^13 - 2236416*x^11 + 2196480*x^9 - 1013760*x^7 + 221760*x^5 -… 2026-08-09 — flattening
3 14 1966080*x^14 - 5591040*x^12 + 6150144*x^10 - 3294720*x^8 + 887040*x^6… 2026-08-09 — flattening
3 15 4456448*x^15 - 13762560*x^13 + 16773120*x^11 - 10250240*x^9 + 3294720… 2026-08-09 — flattening
3 16 10027008*x^16 - 33423360*x^14 + 44728320*x^12 - 30750720*x^10 + 11531… 2026-08-09 — flattening
3 17 22413312*x^17 - 80216064*x^15 + 116981760*x^13 - 89456640*x^11 + 3843… 2026-08-09 — flattening
3 18 49807360*x^18 - 190513152*x^16 + 300810240*x^14 - 253460480*x^12 + 12… 2026-08-09 — flattening
3 19 110100480*x^19 - 448266240*x^17 + 762052608*x^15 - 701890560*x^13 + 3… 2026-08-09 — flattening
3 20 242221056*x^20 - 1045954560*x^18 + 1905131520*x^16 - 1905131520*x^14 … 2026-08-09 — flattening
7/2 0 1 2026-08-09 — flattening
7/2 1 7*x 2026-08-09 — flattening
7/2 2 63/2*x^2 - 7/2 2026-08-09 — flattening
7/2 3 231/2*x^3 - 63/2*x 2026-08-09 — flattening
7/2 4 3003/8*x^4 - 693/4*x^2 + 63/8 2026-08-09 — flattening
7/2 5 9009/8*x^5 - 3003/4*x^3 + 693/8*x 2026-08-09 — flattening
7/2 6 51051/16*x^6 - 45045/16*x^4 + 9009/16*x^2 - 231/16 2026-08-09 — flattening
7/2 7 138567/16*x^7 - 153153/16*x^5 + 45045/16*x^3 - 3003/16*x 2026-08-09 — flattening
7/2 8 2909907/128*x^8 - 969969/32*x^6 + 765765/64*x^4 - 45045/32*x^2 + 3003… 2026-08-09 — flattening
7/2 9 7436429/128*x^9 - 2909907/32*x^7 + 2909907/64*x^5 - 255255/32*x^3 + 4… 2026-08-09 — flattening
7/2 10 37182145/256*x^10 - 66927861/256*x^8 + 20369349/128*x^6 - 4849845/128… 2026-08-09 — flattening
7/2 11 91265265/256*x^11 - 185910725/256*x^9 + 66927861/128*x^7 - 20369349/1… 2026-08-09 — flattening
7/2 12 882230895/1024*x^12 - 1003917915/512*x^10 + 1673196525/1024*x^8 - 156… 2026-08-09 — flattening
7/2 13 2103781365/1024*x^13 - 2646692685/512*x^11 + 5019589575/1024*x^9 - 55… 2026-08-09 — flattening
7/2 14 9917826435/2048*x^14 - 27349157745/2048*x^12 + 29113619535/2048*x^10 … 2026-08-09 — flattening
7/2 15 23141595015/2048*x^15 - 69424785045/2048*x^13 + 82047473235/2048*x^11… 2026-08-09 — flattening
7/2 16 856239015555/32768*x^16 - 347123925225/4096*x^14 + 902522205585/8192*… 2026-08-09 — flattening
7/2 17 1964313035685/32768*x^17 - 856239015555/4096*x^15 + 2429867476575/819… 2026-08-09 — flattening
7/2 18 8948537162565/65536*x^18 - 33393321606645/65536*x^16 + 12843585233325… 2026-08-09 — flattening
7/2 19 20251952525805/65536*x^19 - 80536834463085/65536*x^17 + 3339332160664… 2026-08-09 — flattening
7/2 20 182267572732245/262144*x^20 - 384787097990295/131072*x^18 + 136912618… 2026-08-09 — flattening
4 0 1 2026-08-09 — flattening
4 1 8*x 2026-08-09 — flattening
4 2 40*x^2 - 4 2026-08-09 — flattening
4 3 160*x^3 - 40*x 2026-08-09 — flattening
4 4 560*x^4 - 240*x^2 + 10 2026-08-09 — flattening
4 5 1792*x^5 - 1120*x^3 + 120*x 2026-08-09 — flattening
4 6 5376*x^6 - 4480*x^4 + 840*x^2 - 20 2026-08-09 — flattening
4 7 15360*x^7 - 16128*x^5 + 4480*x^3 - 280*x 2026-08-09 — flattening
4 8 42240*x^8 - 53760*x^6 + 20160*x^4 - 2240*x^2 + 35 2026-08-09 — flattening
4 9 112640*x^9 - 168960*x^7 + 80640*x^5 - 13440*x^3 + 560*x 2026-08-09 — flattening
4 10 292864*x^10 - 506880*x^8 + 295680*x^6 - 67200*x^4 + 5040*x^2 - 56 2026-08-09 — flattening
4 11 745472*x^11 - 1464320*x^9 + 1013760*x^7 - 295680*x^5 + 33600*x^3 - 10… 2026-08-09 — flattening
4 12 1863680*x^12 - 4100096*x^10 + 3294720*x^8 - 1182720*x^6 + 184800*x^4 … 2026-08-09 — flattening
4 13 4587520*x^13 - 11182080*x^11 + 10250240*x^9 - 4392960*x^7 + 887040*x^… 2026-08-09 — flattening
4 14 11141120*x^14 - 29818880*x^12 + 30750720*x^10 - 15375360*x^8 + 384384… 2026-08-09 — flattening
4 15 26738688*x^15 - 77987840*x^13 + 89456640*x^11 - 51251200*x^9 + 153753… 2026-08-09 — flattening
4 16 63504384*x^16 - 200540160*x^14 + 253460480*x^12 - 164003840*x^10 + 57… 2026-08-09 — flattening
4 17 149422080*x^17 - 508035072*x^15 + 701890560*x^13 - 506920960*x^11 + 2… 2026-08-09 — flattening
4 18 348651520*x^18 - 1270087680*x^16 + 1905131520*x^14 - 1520762880*x^12 … 2026-08-09 — flattening
4 19 807403520*x^19 - 3137863680*x^17 + 5080350720*x^15 - 4445306880*x^13 … 2026-08-09 — flattening
4 20 1857028096*x^20 - 7670333440*x^18 + 13335920640*x^16 - 12700876800*x^… 2026-08-09 — flattening