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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{17}-\frac{3855458534}{18122395}\cdot t^{15}+\frac{76689404679}{18122395}\cdot t^{13}-\frac{1451963624397}{36244790}\cdot t^{11}+\frac{2765036333631}{14497916}\cdot t^9-\frac{12957851045997}{28995832}\cdot t^7+\frac{27641768331177}{57991664}\cdot t^5-\frac{23638263740091}{115983328}\cdot t^3+\frac{3232373443299}{115983328}\cdot t$
• $P_4$:
  $4\cdot t^{37}-\frac{275770854121382311206376023705664310036315616984765272017803000660420653253793520853735703223839942118090838}{296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015}\cdot t^{35}+\frac{28401865784716907268077654505005876097810837471748400964181150772250851140807280076221697317810624865462795563}{296246896185710938304554200393915299263986747233743795083330865212148833473368091501155397420631665875015}\cdot t^{33}-\frac{3429045819264892772698962900221791065307139422256570722901911899410360071343163074391597045572010496169312593329}{592493792371421876609108400787830598527973494467487590166661730424297666946736183002310794841263331750030}\cdot t^{31}+\frac{54191795693746139715063552146702609120600365696976827935532647393032468854229089011799596564796372640135068605237}{236997516948568750643643360315132239411189397786995036066664692169719066778694473200924317936505332700012}\cdot t^{29}-\frac{2964381279369501701809614173664502854362094572701530434214881236744562824941150458294545548979806479039860459956747}{473995033897137501287286720630264478822378795573990072133329384339438133557388946401848635873010665400024}\cdot t^{27}+\frac{115813400216063060540306092187747016522028385895236684244477115973650558395235893704582765081533984435177483891468251}{947990067794275002574573441260528957644757591147980144266658768678876267114777892803697271746021330800048}\cdot t^{25}-\frac{3287202806406687286268138519862366893951135669346210638778578946679197500624803911213277240215680990033086664771003769}{1895980135588550005149146882521057915289515182295960288533317537357752534229555785607394543492042661600096}\cdot t^{23}+\frac{68306496467102120852281737301604522784094306835252244244320161215213867080985316241915022378589191543568194466569428567}{3791960271177100010298293765042115830579030364591920577066635074715505068459111571214789086984085323200192}\cdot t^{21}-\frac{1039493849531555969960377470180425722399144022787714873318254047561873426704197696529357090918994447510354158188036475285}{7583920542354200020596587530084231661158060729183841154133270149431010136918223142429578173968170646400384}\cdot t^{19}+\frac{11514023597923209516375958316968114306303072432688887822303613002551747106248655677113953252165599823398609778992272726445}{15167841084708400041193175060168463322316121458367682308266540298862020273836446284859156347936341292800768}\cdot t^{17}-\frac{91638700727372879598684525814340388215359457769385669078923474187943867527577112601072928850984355228880973370320231719655}{30335682169416800082386350120336926644632242916735364616533080597724040547672892569718312695872682585601536}\cdot t^{15}+\frac{513292406290775689709898294056809060361284241014944920166560319543435028218719892044852013150619956767040482138922313800855}{60671364338833600164772700240673853289264485833470729233066161195448081095345785139436625391745365171203072}\cdot t^{13}-\frac{1961709479044381440148093600801797722990561355937816179577321889743194724618569617777320335732421664803744592311233461713065}{121342728677667200329545400481347706578528971666941458466132322390896162190691570278873250783490730342406144}\cdot t^{11}+\frac{4889399494554241310261405047869067703214016505518883005993457070423397086230265565886769244982985401313532697692047075345225}{242685457355334400659090800962695413157057943333882916932264644781792324381383140557746501566981460684812288}\cdot t^9-\frac{7447055826185708139971679984325950995709190795250496319355685363719159173238792939229441119467985844518011222418309742039075}{485370914710668801318181601925390826314115886667765833864529289563584648762766281115493003133962921369624576}\cdot t^7+\frac{3170700591423806624411609215186459350086448052306705693902148802688446331495402334142209940365807284121874672246654702933025}{485370914710668801318181601925390826314115886667765833864529289563584648762766281115493003133962921369624576}\cdot t^5-\frac{337101196512942568187414759798559915335990263525098771070385072482317690522500952292046849821082139187342197777671382414225}{242685457355334400659090800962695413157057943333882916932264644781792324381383140557746501566981460684812288}\cdot t^3+\frac{1728831376655429028767577783003269839498677363940547128483187839547869954649866480195142345281119085400882067830936771775}{15167841084708400041193175060168463322316121458367682308266540298862020273836446284859156347936341292800768}\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 (physicists') type can be downloaded here packed into a single file.