Rule: Q[2, 20, 31]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{22}-\frac{1181590807}{5060457}\cdot t^{20}+\frac{113450524465}{5060457}\cdot t^{18}-\frac{649682892835}{562273}\cdot t^{16}+\frac{19694384411050}{562273}\cdot t^{14}-\frac{362148733074310}{562273}\cdot t^{12}+\frac{4024456368542610}{562273}\cdot t^{10}-\frac{26133921471007350}{562273}\cdot t^8+\frac{92387182004842725}{562273}\cdot t^6-\frac{155509398101932875}{562273}\cdot t^4+\frac{94224095717476725}{562273}\cdot t^2-\frac{8649322961253975}{562273}$
• $P_3$:
  $t^{53}-\frac{5163279899880145920446043835400887836994552131949118339830795950325427338957036064118581444041725302747497567963664260588628587387183575043549536677131713389}{5404159799055435486200467120253998323182160268920284226411178949149693719335043207783008766473831178707447685188889536121822341672840292262825797021749739}\cdot t^{51}+\frac{2265867571722158887654231805282546235988787618799798516224180923521176221508149692840702568944739332354141727962492507663332873665718209303394732482437453812975}{5404159799055435486200467120253998323182160268920284226411178949149693719335043207783008766473831178707447685188889536121822341672840292262825797021749739}\cdot t^{49}-\frac{202354964828658865628072948746138205970802326380324456531639144415145649021662910390989667447639390414380630816636154981559111495874743423139995357298779157778875}{1801386599685145162066822373417999441060720089640094742137059649716564573111681069261002922157943726235815895062963178707274113890946764087608599007249913}\cdot t^{47}+\frac{12370139340935281628239628721146882414326420347531018186235844080287502647393838059742915945829616111243771255708542976616387725031918825304527132423699120360603575}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{45}-\frac{1650380319192726146552185947300829852186805837653124107311250008053098098690703056859596078061480412256098852244236914215552325017224242909918581021199710662108864645}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{43}+\frac{166199205738125459210126020265083697093990694676955617019623539998115703109572064975035565445187570748579125320754205301695677214921930057226308666229925932139542470145}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{41}-\frac{12937870543632799204859885075421016737064326667596187123420653632619337657453997300651202529585127748143239787504534503262621916346969314317645370396119472272390363192175}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{39}+\frac{790992930421377828832735407695112372382014138070054877210378751760647036817367784029564047961933548027461880311098236247316703774962091029997604725029542707790001911004300}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{37}-\frac{38380504637906360156676739275096540969930461918359684169899197187992720560100469037454359938423027722195494790379048813559081682925590146540648777217930864731850404977233000}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{35}+\frac{1487737116104896964848723942815653345940147965621122600266420270419359113982360139903837319317536916314363572586903094928985135844133505792683467037620555771734965821477893950}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{33}-\frac{46230708039517158911028200704645873737069832513508755470006706409088674541311249823528259713544975466488865380130419784306772069459486805253816995584256139847023415757906647450}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{31}+\frac{1152672795581521465777136344482013894184472652838150408518192389657135382510277140422415778125322516235834140003342134409860843944326176028983222606147338108781382527818202494750}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{29}-\frac{23025653189274955605096820606310229160903222826247200478125020466732178722800674961324258630841636418810227194532216790757690613102428360057986966876298472280704243991217688132250}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{27}+\frac{367125114500320416478759258411641622853158193252293978644554961731695853952153234403243308094826997671800082323833606631995553788743759384793969422526140219136513677089071716381250}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{25}-\frac{4643527965614310520932242952516706397838009188161761678251842674310860514689253918594588685596422814405045780012759196214118676528033155404179750662233159095503772414711978060298750}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{23}+\frac{46186445739183703293799506219348558661592599740000019648176048723641326272319707483808075012060394853675668572099318731194320479077148448139424536202133377262805312543267311979926875}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{21}-\frac{357020520952150847920974298540747365281814813524811272889718518170370296677393952372525598711503584597792402558805772921961867225735618244409812207267229170019538313107172000354053125}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{19}+\frac{2111772451905025015481706147121278014198206422359459720025540694089332622642032949096526412575166564637846275681492841991335565151069403155663792050797401784046178700276410279058271875}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{17}-\frac{9366313377819671837456038061137718072516954727801965372694337790553889472583033331767555377604898635288484934559204526047547475693932984883082545497343790944856965752273839985015078125}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{15}+\frac{30331014278913628028736403665207220524402789057361136296385690452346791643704133685858234566230879184833925352243885424916386250732673200579358457066204084367266072855524456719267746875}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{13}-\frac{69218370912653121745074519799696857120673793606664942912031748998223749587236717129713547925928566924560749173758915544189511751118926190312529969474944961820058891328216729633339340625}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^{11}+\frac{106123620801764603315241861471025770216245982475329712523814043250577548261497627164106945242643987424617828315345720512191411221319014813444821129156624503081401094330503343262247078125}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^9-\frac{102322561894814494881300820204600771796203970834541423555500493670486341296671482329027492376247458785770558073481051498329429006477572795088721015479876128983074135017059864572083171875}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^7+\frac{56236723618242731265776877739536811886366479015729227674114976617109831607180804350648050739794388705300132989190217351752639009267225559756750769726857275272437135429656122947926093750}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^5-\frac{14636028398379816839329807739469843006106391184419280656199569029363929010610354324794868592254223581578588756510727152561072044211427528557665987958147111328420146544201897841401718750}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t^3+\frac{1055275828666165714519266581211709000336426799259512625670416035935519572252492304151008883406595759859137634020594131157358626712692032876326212505889757263227959943881643591844375000}{600462199895048387355607457805999813686906696546698247379019883238854857703893689753667640719314575411938631687654392902424704630315588029202866335749971}\cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.