Rule: Q[2, 3, 12, 20]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{17}-\frac{1927729267}{18122395}\cdot t^{15}+\frac{76689404679}{18122395}\cdot t^{13}-\frac{1451963624397}{18122395}\cdot t^{11}+\frac{2765036333631}{3624479}\cdot t^9-\frac{12957851045997}{3624479}\cdot t^7+\frac{27641768331177}{3624479}\cdot t^5-\frac{23638263740091}{3624479}\cdot t^3+\frac{6464746886598}{3624479}\cdot t$
• $P_4$:
  $t^{37}-\frac{137885427060691155603188011852832155018157808492382636008901500330210326626896760426867851611919971059045419}{296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015}\cdot t^{35}+\frac{28401865784716907268077654505005876097810837471748400964181150772250851140807280076221697317810624865462795563}{296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015}\cdot t^{33}-\frac{3429045819264892772698962900221791065307139422256570722901911899410360071343163074391597045572010496169312593329}{296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015}\cdot t^{31}+\frac{54191795693746139715063552146702609120600365696976827935532647393032468854229089011799596564796372640135068605237}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{29}-\frac{2964381279369501701809614173664502854362094572701530434214881236744562824941150458294545548979806479039860459956747}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{27}+\frac{115813400216063060540306092187747016522028385895236684244477115973650558395235893704582765081533984435177483891468251}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{25}-\frac{3287202806406687286268138519862366893951135669346210638778578946679197500624803911213277240215680990033086664771003769}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{23}+\frac{68306496467102120852281737301604522784094306835252244244320161215213867080985316241915022378589191543568194466569428567}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{21}-\frac{1039493849531555969960377470180425722399144022787714873318254047561873426704197696529357090918994447510354158188036475285}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{19}+\frac{11514023597923209516375958316968114306303072432688887822303613002551747106248655677113953252165599823398609778992272726445}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{17}-\frac{91638700727372879598684525814340388215359457769385669078923474187943867527577112601072928850984355228880973370320231719655}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{15}+\frac{513292406290775689709898294056809060361284241014944920166560319543435028218719892044852013150619956767040482138922313800855}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{13}-\frac{1961709479044381440148093600801797722990561355937816179577321889743194724618569617777320335732421664803744592311233461713065}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^{11}+\frac{4889399494554241310261405047869067703214016505518883005993457070423397086230265565886769244982985401313532697692047075345225}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^9-\frac{7447055826185708139971679984325950995709190795250496319355685363719159173238792939229441119467985844518011222418309742039075}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^7+\frac{6341401182847613248823218430372918700172896104613411387804297605376892662990804668284419880731614568243749344493309405866050}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^5-\frac{2696809572103540545499318078388479322687922108200790168563080579858541524180007618336374798568657113498737582221371059313800}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\cdot t^3+\frac{442580832423789831364499912448837078911661405168780064891696086924254708390365818929956440391966485862625809364719813574400}{59249379237142187660910840078783059852797349446748759016666173042429766694673618300231079484126333175003}\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.