Hermite polynomials in physicist's convention
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Polynomials
$n$ 
$H_n(x)$
0:
1
1:
2*x
2:
4*x^2 - 2
3:
8*x^3 - 12*x
4:
16*x^4 - 48*x^2 + 12
5:
32*x^5 - 160*x^3 + 120*x
6:
64*x^6 - 480*x^4 + 720*x^2 - 120
7:
128*x^7 - 1344*x^5 + 3360*x^3 - 1680*x
8:
256*x^8 - 3584*x^6 + 13440*x^4 - 13440*x^2 + 1680
9:
512*x^9 - 9216*x^7 + 48384*x^5 - 80640*x^3 + 30240*x
10:
1024*x^10 - 23040*x^8 + 161280*x^6 - 403200*x^4 + 302400*x^2 - 30240
11:
2048*x^11 - 56320*x^9 + 506880*x^7 - 1774080*x^5 + 2217600*x^3 - 665280*x
12:
4096*x^12 - 135168*x^10 + 1520640*x^8 - 7096320*x^6 + 13305600*x^4 - 7983360*x^2 + 665280
13:
8192*x^13 - 319488*x^11 + 4392960*x^9 - 26357760*x^7 + 69189120*x^5 - 69189120*x^3 + 17297280*x
14:
16384*x^14 - 745472*x^12 + 12300288*x^10 - 92252160*x^8 + 322882560*x^6 - 484323840*x^4 + 242161920*x^2 - 17297280
15:
32768*x^15 - 1720320*x^13 + 33546240*x^11 - 307507200*x^9 + 1383782400*x^7 - 2905943040*x^5 + 2421619200*x^3 - 518918400*x
16:
65536*x^16 - 3932160*x^14 + 89456640*x^12 - 984023040*x^10 + 5535129600*x^8 - 15498362880*x^6 + 19372953600*x^4 - 8302694400*x^2 + 518918400
17:
131072*x^17 - 8912896*x^15 + 233963520*x^13 - 3041525760*x^11 + 20910489600*x^9 - 75277762560*x^7 + 131736084480*x^5 - 94097203200*x^3 + 17643225600*x
18:
262144*x^18 - 20054016*x^16 + 601620480*x^14 - 9124577280*x^12 + 75277762560*x^10 - 338749931520*x^8 + 790416506880*x^6 - 846874828800*x^4 + 317578060800*x^2 - 17643225600
19:
524288*x^19 - 44826624*x^17 + 1524105216*x^15 - 26671841280*x^13 + 260050452480*x^11 - 1430277488640*x^9 + 4290832465920*x^7 - 6436248698880*x^5 + 4022655436800*x^3 - 670442572800*x
20:
1048576*x^20 - 99614720*x^18 + 3810263040*x^16 - 76205260800*x^14 + 866834841600*x^12 - 5721109954560*x^10 + 21454162329600*x^8 - 42908324659200*x^6 + 40226554368000*x^4 - 13408851456000*x^2 + 670442572800
21:
2097152*x^21 - 220200960*x^19 + 9413591040*x^17 - 213374730240*x^15 + 2800543334400*x^13 - 21844238008320*x^11 + 100119424204800*x^9 - 257449947955200*x^7 + 337903056691200*x^5 - 187723920384000*x^3 + 28158588057600*x
22:
4194304*x^22 - 484442112*x^20 + 23011000320*x^18 - 586780508160*x^16 + 8801707622400*x^14 - 80095539363840*x^12 + 440525466501120*x^10 - 1415974713753600*x^8 + 2477955749068800*x^6 - 2064963124224000*x^4 + 619488937267200*x^2 - 28158588057600
23:
8388608*x^23 - 1061158912*x^21 + 55710842880*x^19 - 1587759022080*x^17 + 26991903375360*x^15 - 283414985441280*x^13 + 1842197405368320*x^11 - 7237204092518400*x^9 + 16283709208166400*x^7 - 18997660742860800*x^5 + 9498830371430400*x^3 - 1295295050649600*x
24:
16777216*x^24 - 2315255808*x^22 + 133706022912*x^20 - 4234024058880*x^18 + 80975710126080*x^16 - 971708521512960*x^14 + 7368789621473280*x^12 - 34738579644088320*x^10 + 97702255248998400*x^8 - 151981285942886400*x^6 + 113985964457164800*x^4 - 31087081215590400*x^2 + 1295295050649600
25:
33554432*x^25 - 5033164800*x^23 + 318347673600*x^21 - 11142168576000*x^19 + 238163853312000*x^17 - 3239028405043200*x^15 + 28341498544128000*x^13 - 157902634745856000*x^11 + 542790306938880000*x^9 - 1085580613877760000*x^7 + 1139859644571648000*x^5 - 518118020259840000*x^3 + 64764752532480000*x
26:
67108864*x^26 - 10905190400*x^24 + 752458137600*x^22 - 28969638297600*x^20 + 688028909568000*x^18 - 10526842316390400*x^16 + 105268423163904000*x^14 - 684244750565376000*x^12 + 2822509596082176000*x^10 - 7056273990205440000*x^8 + 9878783586287616000*x^6 - 6735534263377920000*x^4 + 1683883565844480000*x^2 - 64764752532480000
27:
134217728*x^27 - 23555211264*x^25 + 1766640844800*x^23 - 74493355622400*x^21 + 1955450585088000*x^19 - 33438205005004800*x^17 + 378966323390054400*x^15 - 2842247425425408000*x^13 + 13855956198948864000*x^11 - 42337643941232640000*x^9 + 76207759094218752000*x^7 - 72743770044481536000*x^5 + 30309904185200640000*x^3 - 3497296636753920000*x
28:
268435456*x^28 - 50734301184*x^26 + 4122161971200*x^24 - 189619450675200*x^22 + 5475261638246400*x^20 - 104029971126681600*x^18 + 1326382131865190400*x^16 - 11368989701701632000*x^14 + 64661128928428032000*x^12 - 237090806070902784000*x^10 + 533454313659531264000*x^8 - 678941853748494336000*x^6 + 424338658592808960000*x^4 - 97924305829109760000*x^2 + 3497296636753920000
29:
536870912*x^29 - 108984795136*x^27 + 9563415773184*x^25 - 478170788659200*x^23 + 15122151191347200*x^21 - 317565175018291200*x^19 + 4525303744010649600*x^17 - 43960093513246310400*x^15 + 288488113680678912000*x^13 - 1250115159282941952000*x^11 + 3437816688028090368000*x^9 - 5625518216773238784000*x^7 + 4922328439676583936000*x^5 - 1893203246029455360000*x^3 + 202843204931727360000*x
30:
1073741824*x^30 - 233538846720*x^28 + 22069421015040*x^26 - 1195426971648000*x^24 + 41242230521856000*x^22 - 952695525054873600*x^20 + 15084345813368832000*x^18 - 164850350674673664000*x^16 + 1236377630060052480000*x^14 - 6250575796414709760000*x^12 + 20626900128168542208000*x^10 - 42191386625799290880000*x^8 + 49223284396765839360000*x^6 - 28398048690441830400000*x^4 + 6085296147951820800000*x^2 - 202843204931727360000
31:
2147483648*x^31 - 499289948160*x^29 + 50677929738240*x^27 - 2964658889687040*x^25 + 111174708363264000*x^23 - 2812720121590579200*x^21 + 49222602127835136000*x^19 - 601218925989986304000*x^17 + 5110360870914883584000*x^15 - 29810438413670154240000*x^13 + 116260709813313601536000*x^11 - 290651774533284003840000*x^9 + 435977661799926005760000*x^7 - 352135803761478696960000*x^5 + 125762787057670963200000*x^3 - 12576278705767096320000*x
32:
4294967296*x^32 - 1065151889408*x^30 + 115835267973120*x^28 - 7297621882306560*x^26 + 296465888968704000*x^24 - 8182458535536230400*x^22 + 157512326809072435200*x^20 - 2137667292408840192000*x^18 + 20441443483659534336000*x^16 - 136276289891063562240000*x^14 + 620057119004339208192000*x^12 - 1860171357013017624576000*x^10 + 3487821294399408046080000*x^8 - 3756115240122439434240000*x^6 + 2012204592922735411200000*x^4 - 402440918584547082240000*x^2 + 12576278705767096320000
33:
8589934592*x^33 - 2267742732288*x^31 + 263625092628480*x^29 - 17838631267860480*x^27 + 782669946877378560*x^25 - 23480098406321356800*x^23 + 495038741399941939200*x^21 - 7425581120999129088000*x^19 + 79360898230678192128000*x^17 - 599615675520679673856000*x^15 + 3147982296483568287744000*x^13 - 11161028142078105747456000*x^11 + 25577356158928992337920000*x^9 - 35414800835440143237120000*x^7 + 26561100626580107427840000*x^5 - 8853700208860035809280000*x^3 + 830034394580628357120000*x
34:
17179869184*x^34 - 4818953306112*x^32 + 597550209957888*x^30 - 43322390221946880*x^28 + 2046982937986990080*x^26 - 66526945484577177600*x^24 + 1530119746145275084800*x^22 - 25246975811397038899200*x^20 + 299807837760339836928000*x^18 - 2548366620962888613888000*x^16 + 15290199725777331683328000*x^14 - 63245826138442599235584000*x^12 + 173926021880717147897856000*x^10 - 301025807101241217515520000*x^8 + 301025807101241217515520000*x^6 - 150512903550620608757760000*x^4 + 28221169415741364142080000*x^2 - 830034394580628357120000
35:
34359738368*x^35 - 10222022164480*x^33 + 1349306925711360*x^31 - 104571286742630400*x^29 + 5306992802188492800*x^27 - 186275447356816097280*x^25 + 4656886183920402432000*x^23 - 84156586037990129664000*x^21 + 1104555191748620451840000*x^19 - 10493274321611894292480000*x^17 + 71354265386960881188864000*x^15 - 340554448437767842037760000*x^13 + 1106801957422745486622720000*x^11 - 2341311833009653914009600000*x^9 + 3010258071012412175155200000*x^7 - 2107180649708688522608640000*x^5 + 658493953033965163315200000*x^3 - 58102407620643984998400000*x
36:
68719476736*x^36 - 21646635171840*x^34 + 3035940582850560*x^32 - 250971088182312960*x^30 + 13646552919913267200*x^28 - 515839700372721500160*x^26 + 13970658551761207296000*x^24 - 275421554306149515264000*x^22 + 3976398690295033626624000*x^20 - 41973097286447577169920000*x^18 + 321094194241323965349888000*x^16 - 1751422877679948901908480000*x^14 + 6640811744536472919736320000*x^12 - 16857445197669508180869120000*x^10 + 27092322639111709576396800000*x^8 - 25286167796504262271303680000*x^6 + 11852891154611372939673600000*x^4 - 2091686674343183459942400000*x^2 + 58102407620643984998400000
37:
137438953472*x^37 - 45767171506176*x^35 + 6807866761543680*x^33 - 599092275015843840*x^31 + 34822238485295923200*x^29 - 1413782882503014481920*x^27 + 41353149313213173596160*x^25 - 886138913854568005632000*x^23 + 14012071575325356589056000*x^21 - 163474168378795826872320000*x^19 + 1397704139638704319758336000*x^17 - 8640352863221081249415168000*x^15 + 37801543776592230466191360000*x^13 - 113404631329776691398574080000*x^11 + 222759097254918500961484800000*x^9 - 267310916705902201153781760000*x^7 + 175422789088248319507169280000*x^5 - 51594937967131858678579200000*x^3 + 4299578163927654889881600000*x
38:
274877906944*x^38 - 96619584290816*x^36 + 15217584525803520*x^34 - 1422844153162629120*x^32 + 88216337496083005440*x^30 - 3837410681079610736640*x^28 + 120878436454007738204160*x^26 - 2806106560539465351168000*x^24 + 48405338169305777307648000*x^22 - 621201839839424142114816000*x^20 + 5901417478474529350090752000*x^18 - 41041676100300135934722048000*x^16 + 205208380501500679673610240000*x^14 - 718229331755252378857635840000*x^12 + 1692969139137380607307284480000*x^10 - 2539453708706070910960926720000*x^8 + 2222021995117812047090810880000*x^6 - 980303821375505314893004800000*x^4 + 163383970229250885815500800000*x^2 - 4299578163927654889881600000
39:
549755813888*x^39 - 203684529045504*x^37 + 33913474086076416*x^35 - 3363086180202577920*x^33 + 221963687893370142720*x^31 - 10321311487041711636480*x^29 + 349204371978244577034240*x^27 - 8755052468883131895644160*x^25 + 164157233791558723043328000*x^23 - 2307321119403575384997888000*x^21 + 24226871753737541542477824000*x^19 - 188308866813141800171077632000*x^17 + 1067083578607803534302773248000*x^15 - 4309375990531514273145815040000*x^13 + 12004690259337789760906199040000*x^11 - 22008598808785947894994698240000*x^9 + 24759673659884191381869035520000*x^7 - 15292739613457882912330874880000*x^5 + 4247983225960523031203020800000*x^3 - 335367096786357081410764800000*x
40:
1099511627776*x^40 - 428809534832640*x^38 + 75363275746836480*x^36 - 7913143953417830400*x^34 + 554909219733425356800*x^32 - 27523497298777897697280*x^30 + 997726777080698791526400*x^28 - 26938622981178867371212800*x^26 + 547190779305195743477760000*x^24 - 8390258616013001399992320000*x^22 + 96907487014950166169911296000*x^20 - 836928296947296889649233920000*x^18 + 5335417893039017671513866240000*x^16 - 24625005660180081560833228800000*x^14 + 80031268395585265072707993600000*x^12 - 176068790470287583159957585920000*x^10 + 247596736598841913818690355200000*x^8 - 203903194846105105497744998400000*x^6 + 84959664519210460624060416000000*x^4 - 13414683871454283256430592000000*x^2 + 335367096786357081410764800000
41:
2199023255552*x^41 - 901599534776320*x^39 + 167021313817313280*x^37 - 18539365833721774080*x^35 + 1378865333883056947200*x^33 - 72804089629025406812160*x^31 + 2821158473124734513971200*x^29 - 81813595720617300905164800*x^27 + 1794785756121042038607052800*x^25 - 29913095935350700643450880000*x^23 + 378400663582186363139653632000*x^21 - 3612006334193597102696693760000*x^19 + 25735545131129379356713943040000*x^17 - 134616697608984445865888317440000*x^15 + 504812616033691671997081190400000*x^13 - 1312512801687598347192411095040000*x^11 + 2255881377900559659236956569600000*x^9 - 2388580282482945521545012838400000*x^7 + 1393338498115051554234590822400000*x^5 - 366668025819750409009102848000000*x^3 + 27500101936481280675682713600000*x
42:
4398046511104*x^42 - 1893359023030272*x^40 + 369205009490903040*x^38 - 43258520278684139520*x^36 + 3406608471946375987200*x^34 - 191110735276191692881920*x^32 + 7899243724749256639119360*x^30 - 245440787161851902715494400*x^28 + 5798538596698751201653555200*x^26 - 104695835773727452252078080000*x^24 + 1444802533677438841078677504000*x^22 - 15170426603613107831326113792000*x^20 + 120099210611937103664665067520000*x^18 - 706737662447168340795913666560000*x^16 + 3028875696202150031982487142400000*x^14 - 9187589611813188430346877665280000*x^12 + 18949403574364701137590435184640000*x^10 - 25080092966070927976222634803200000*x^8 + 19506738973610721759284271513600000*x^6 - 7700028542214758589191159808000000*x^4 + 1155004281332213788378673971200000*x^2 - 27500101936481280675682713600000
43:
8796093022208*x^43 - 3971435999526912*x^41 + 814144379903016960*x^39 - 100546830918022594560*x^37 + 8370523673925380997120*x^35 - 498046158598560169328640*x^33 + 21914030978336647450460160*x^31 - 727858886066181504604569600*x^29 + 18469419233929355679340953600*x^27 - 360153675061622435747148595200*x^25 + 5402305125924336536207228928000*x^23 - 62126508948129870166383132672000*x^21 + 543606953296136363955852410880000*x^19 - 3575261115909204547555798548480000*x^17 + 17365553991558993516699592949760000*x^15 - 60779438970456477308448575324160000*x^13 + 148149882490487663439343402352640000*x^11 - 239654221675788867328349621452800000*x^9 + 239654221675788867328349621452800000*x^7 - 132440490926093847734087948697600000*x^5 + 33110122731523461933521987174400000*x^3 - 2365008766537390138108713369600000*x
44:
17592186044416*x^44 - 8321103999008768*x^42 + 1791117635786637312*x^40 - 232845292652262850560*x^38 + 20461280091817597992960*x^36 - 1289060645784508673556480*x^34 + 60263585190425780488765440*x^32 - 2135052732460799080173404160*x^30 + 58046746163777974992214425600*x^28 - 1218981669439337474836502937600*x^26 + 19808452128389233966093172736000*x^24 - 248506035792519480665532530688000*x^22 + 2391870594503000001405750607872000*x^20 - 17479054344445000010272792903680000*x^18 + 95510546953574464341847761223680000*x^16 - 382042187814297857367391044894720000*x^14 + 1086432471596909531888518283919360000*x^12 - 2108957150746942032489476668784640000*x^10 + 2636196438433677540611845835980800000*x^8 - 1942460533582709766766623247564800000*x^6 + 728422700093516162537483717836800000*x^4 - 104060385727645166076783388262400000*x^2 + 2365008766537390138108713369600000
45:
35184372088832*x^45 - 17416264183971840*x^43 + 3931721639531642880*x^41 - 537335290735991193600*x^39 + 49770681304421184307200*x^37 - 3314727374874450874859520*x^35 + 164355232337524855878451200*x^33 - 6198540191015223135987302400*x^31 + 180145074301379922389630976000*x^29 - 4063272231464458249455009792000*x^27 + 71310427662201242277935421849600*x^25 - 972414922666380576517301207040000*x^23 + 10250873976441428577453216890880000*x^21 - 82795520578950000048660597964800000*x^19 + 505644072107158928868605794713600000*x^17 - 2292253126885787144204346269368320000*x^15 + 7521455572593989066920511196364800000*x^13 - 17255103960656798447641172744601600000*x^11 + 26361964384336775406118458359808000000*x^9 - 24974492574634839858428013182976000000*x^7 + 13111608601683290925674706921062400000*x^5 - 3121811571829354982303501647872000000*x^3 + 212850788988365112429784203264000000*x
46:
70368744177664*x^46 - 36415825111941120*x^44 + 8612342638974074880*x^42 - 1235871168692779745280*x^40 + 120497438947546025164800*x^38 - 8470969958012485569085440*x^36 + 444725922795655492376985600*x^34 - 17820803049168766515963494400*x^32 + 552444894524231761994868326400*x^30 - 13350751617668934248209317888000*x^28 + 252329205573942857291156108083200*x^26 - 3727590536887792209982987960320000*x^24 + 42867291174209610414804361543680000*x^22 - 380859394663170000223838750638080000*x^20 + 2584403035214367858661762950758400000*x^18 - 13180455479593276079174991048867840000*x^16 + 49426708048474785296906216433254400000*x^14 - 132289130365035454765248991041945600000*x^12 + 242530072335898333736289816910233600000*x^10 - 287206664608300658371922151604224000000*x^8 + 201044665225810460860345506122956800000*x^6 - 71801666152075164592980537901056000000*x^4 + 9791136293464795171770073350144000000*x^2 - 212850788988365112429784203264000000
47:
140737488355328*x^47 - 76068612456054784*x^45 + 18826981582873559040*x^43 - 2833460728222470635520*x^41 + 290429724642803240140800*x^39 - 21520842596031720094433280*x^37 + 1194406764079760465241047040*x^35 - 50762287473389819772744499200*x^33 + 1675155486621864052500568473600*x^31 - 43274850071064821356264685568000*x^29 + 878479456442615873532173117030400*x^27 - 14015740418698098709536034730803200*x^25 + 175196755233726233869200434135040000*x^23 - 1704799195158951429573373455237120000*x^21 + 12785993963692135721800300914278400000*x^19 - 72880165593045173614261715211386880000*x^17 + 309740703770441987860612289648394240000*x^15 - 956552173408717903687185012149452800000*x^13 + 2072529709052222124655567526323814400000*x^11 - 2999714052575584654106742472310784000000*x^9 + 2699742647318026188696068225079705600000*x^7 - 1349871323659013094348034112539852800000*x^5 + 306788937195230248715462298304512000000*x^3 - 20007974164906320568399715106816000000*x
48:
281474976710656*x^48 - 158751886864809984*x^46 + 41077050726269583360*x^44 - 6476481664508504309760*x^42 + 697031339142727776337920*x^40 - 54368444453132766554357760*x^38 + 3185084704212694573976125440*x^36 - 143328811689571255828925644800*x^34 + 5025466459865592157501705420800*x^32 - 138479520227407428340046993817600*x^30 + 3011929564946111566396022115532800*x^28 - 51750426161346826004440743621427200*x^26 + 700787020934904935476801736540160000*x^24 - 7439123760693606238138356895580160000*x^22 + 61372771025722251464641444388536320000*x^20 - 388694216496240925942729147794063360000*x^18 + 1858444222622651927163673737890365440000*x^16 - 6559214903374065625283554369024819200000*x^14 + 16580237672417776997244540210590515200000*x^12 - 28797254904725612679424727734183526400000*x^10 + 32396911767816314264352818700956467200000*x^8 - 21597941178544209509568545800637644800000*x^6 + 7362934492685525969171095159308288000000*x^4 - 960382759915503387283186325127168000000*x^2 + 20007974164906320568399715106816000000
49:
562949953421312*x^49 - 331014572611731456*x^47 + 89456688248320425984*x^45 - 14760353560972870287360*x^43 + 1666074908194812733685760*x^41 - 136618142471974644162232320*x^39 + 8436170297644434277017845760*x^37 - 401320672730799516320991805440*x^35 + 14924112517176607013186882764800*x^33 - 437773967170513805720148561100800*x^31 + 10178244736714445982993454045593600*x^29 - 187834880141184775867970106477772800*x^27 + 2747085122064827347069062807237427200*x^25 - 31697136023824930927719955468124160000*x^23 + 286406264786703840168326740479836160000*x^21 - 2004843853506926881178287183358853120000*x^19 + 10713384342177640521296472136073871360000*x^17 - 42853537368710562085185888544295485440000*x^15 + 124989483992072472748458841587528499200000*x^13 - 256557361878464549325783937995453235200000*x^11 + 352766372582888755322952914743748198400000*x^9 - 302371176499618933133959641208927027200000*x^7 + 144313516056636308995753465122442444800000*x^5 - 31372503490573110651250753287487488000000*x^3 + 1960781468160819415703172080467968000000*x
50:
1125899906842624*x^50 - 689613692941107200*x^48 + 194471061409392230400*x^46 - 33546258093120159744000*x^44 + 3966845019511458889728000*x^42 - 341545356179936610405580800*x^40 + 22200448151695879676362752000*x^38 - 1114779646474443100891643904000*x^36 + 43894448579931197097608478720000*x^34 - 1368043647407855642875464253440000*x^32 + 33927482455714819943311513485312000*x^30 - 670838857647088485242750380277760000*x^28 + 10565712007941643642573318489374720000*x^26 - 132071400099270545532166481117184000000*x^24 + 1301846658121381091674212456726528000000*x^22 - 10024219267534634405891435916794265600000*x^20 + 59518801900986891784980400755965952000000*x^18 - 267834608554441013032411803401846784000000*x^16 + 892782028514803376774706011339489280000000*x^14 - 2137978015653871244381532816628776960000000*x^12 + 3527663725828887553229529147437481984000000*x^10 - 3779639706245236664174495515111587840000000*x^8 + 2405225267610605149929224418707374080000000*x^6 - 784312587264327766281268832187187200000000*x^4 + 98039073408040970785158604023398400000000*x^2 - 1960781468160819415703172080467968000000
Definition
The Hermite polynomials $H_n$, $n\geq 0$, in the physicist's convention, can be defined as $H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2}$.
Parameters
$n$
—   integer ($n \geq 0$)
Formulas
(1)
$H_0(x) = 1$, $H_1(x) = 2x$, and $H_{n+1}(x) = 2x H_n(x) - H_{n}'(x)$ for $n\geq 1$ (recurrence formula).
(2)
$H_n(x) = n!\sum_{k=0}^{[n/2]} \frac{(-1)^k}{k!(n-2k)!} (2x)^{n-2k}$ (closed form).
(3)
$\sum_{n=0}^\infty H_n(x)\frac{t^n}{n!} = e^{2xt-t^2}$ (exponential generating function).
Comments
(4)
The $H_n$ are orthogonal with respect to the inner product $\langle f,g\rangle = \int_{-\infty}^{\infty} f(x)g(x) e^{-x^2/2} dx$.
(5)
$H_n$ relates to the Hermite polynomials in probabilist's convention $He_n$ via $H_n(x) = 2^{n/2} He_n(\sqrt{2}x)$.
Programs
(P1)
Sage
polynomials = {n: hermite(n,x) for n in [0..100]}
Links
Data properties
Entries are of type: integral polynomial
Table is complete: no