Rule: Q[2, 3, 68]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{73}-\frac{1154120410810318360401594366039784397614313659064015275811422403530162920351052261135943}{445642051483281899955200654613299360108122971462033535255939753890254671817396776419}\cdot t^{71}+\frac{1412038085400719672995299756647282535454256254299533153271508475669805619153333310744205293}{445642051483281899955200654613299360108122971462033535255939753890254671817396776419}\cdot t^{69}-\frac{362139236696710845537484203778698205961827450255395791074171020867292200955547558818893119261}{148547350494427299985066884871099786702707657154011178418646584630084890605798925473}\cdot t^{67}+\frac{17888925751906381696411394758243817722500487658261740562143996158216452559290170997391986748998}{13504304590402481816824262261009071518427968832182834401695144057280444600527175043}\cdot t^{65}-\frac{7309065165089505692653947757695445626311876964622324335093065312545859031101488426340490948283640}{13504304590402481816824262261009071518427968832182834401695144057280444600527175043}\cdot t^{63}+\frac{259386420515505830533741725516264540988965123279906637478889544378225090262411045918388681154656520}{1500478287822497979647140251223230168714218759131426044632793784142271622280797227}\cdot t^{61}-\frac{66473584563712648259623507354001403899708688967359429118941167995462852182444930580610193540471161240}{1500478287822497979647140251223230168714218759131426044632793784142271622280797227}\cdot t^{59}+\frac{13922171895134660315575928170149969419969954500033692206124589765915363242535283888295174617134349620340}{1500478287822497979647140251223230168714218759131426044632793784142271622280797227}\cdot t^{57}-\frac{805003731753278402868190553245662467442481031351265085696949803213230388176944323567469312955218950679740}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{55}+\frac{116799846483204550078616208721201961714079136859804858712803464789428944811252685071094479703298550264170100}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{53}-\frac{14278485467995435842844820902780935393356303292864413166353280770068446040954529424256707663915016407430748700}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{51}+\frac{1478514956407134470142672754063015512064491660322800117323861027223165570417664669079277425837113137039151554000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{49}-\frac{130166023923764930714992148710782399497140632466758708266690091835454731211466092794505793812058193926754645179000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{47}+\frac{9766840500320985796941614700543710013483732241843077645831024334340521284390275014262299997691692795361408947397000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{45}-\frac{625403133624763759121441982198440330190311742533115744604191882451932295507169292870514659805976954938693263237375000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{43}+\frac{34185301893117678190605018488148080977592331371900092882733665191760138176687627764471551011870453192281786236427493750}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{41}-\frac{1594060591378679359545765980420589671670714385927401732261955722406571006604869211245956353465485828695643568169332828750}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{39}+\frac{63309787500486354087555163780442652223898769130959700583340530648076501532314672227329872019200751453107045457789597616250}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{37}-\frac{2136253335477355123604983659972737878180566372748614632300500677125503251499164537509041244795229309799226136675051687348750}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{35}+\frac{61031097732604529880613144146937377447308996607845130825207679077626543616774081058057073529334935687512898003200506165612500}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{33}-\frac{1469678673010504170780306350429481891309653180701927391282297043011470762815788541840537277015719522542637354710359770810975000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{31}+\frac{29664146575705484837841235566687334930498770342741210685155599198004485692603107764632707126551456736176979837721365152230425000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{29}-\frac{498411252646153159258608031892013352358275372585639336580048723894610612252230405649750187041194653452087067893334276386147675000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{27}+\frac{6912724369212796579457092827957116209505994952440216581592025223555798987833649969053320693258701960010829014963789671879923837500}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{25}-\frac{78342789119493338995611324225449095951793786066349533399629946641644694430996839770168431518740413640597235657080298243930266937500}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{23}+\frac{716588100818210098184418389928295394460263290515194931859153737648794576609812531687599137632050804103365966942293534946933164812500}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{21}-\frac{5210730032024998138103915045759951806318152819659865155335801465820146043013340245506214694921617753080976202155346308453681245437500}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{19}+\frac{29565154806437669256884216480503075917833653329729277066540923012184315622659487323563643660242512306092635989018444097335782219500000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{17}-\frac{127865235603967618289419879964183365285836445449736759021402753558827137390997723728530062012566973687272859565387387587400016989125000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{15}+\frac{409086737272821298543647356998607662753021066598022878536478457186304316325546174861209891521982024926920667758886657518712398076875000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{13}-\frac{930845890942100349382398871024861727714602250148691979040864738917616263459033205429503651640907481655476477057359074282010514000625000}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^{11}+\frac{1427648121029442503477689756433770511487543962521978289048294093005705750412304835778244713078655461464410456114729846080107329592265625}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^9-\frac{1366260460683850044733374250049956207628886398820050657260109233010211117306441461501541997003086259076407260192083707188993938603203125}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^7+\frac{723767770775258722452797888859177489354604647891261316531604021945067649979559449395372646932201341349957688812424851587720487050234375}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^5-\frac{171899362914707193634979904229707914487325606651824767385312548192305155147137194818301889710169827153348915565575703293840056589453125}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t^3+\frac{11369208414450230656094748177464076973397886460093733524366430923998931059557552803458085837892789157321030155516070773755100303906250}{500159429274165993215713417074410056238072919710475348210931261380757207426932409}\cdot t$

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.