Rule: Q[4, 74]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{78}-\frac{24481550202925782676935738119191663188661247164306390785034771723020595304472}{1073994406589044023830527134094548662600220677749103771540187966884038009}\cdot t^{76}+\frac{578459195422704453775079448267298099867333631777752033279720202825522323783563732}{37589804230616540834068449693309203191007723721218632003906578840941330315}\cdot t^{74}-\frac{246367235710044521935670393068512466818359355577852067579368525006802216209773082566}{37589804230616540834068449693309203191007723721218632003906578840941330315}\cdot t^{72}+\frac{1047254451022169454355900356097859185258334115066807791946101193617029339385500639719}{529433862403049870902372530891678918183207376355192000055022237196356765}\cdot t^{70}-\frac{13629147528296621925560047767906709637560949662730182700078459379036227264861849577687}{30253363565888564051564144622381652467611850077439542860286984982648958}\cdot t^{68}+\frac{4871318349179621162789862988922611015370878412672271412961202975853950184591153413337659}{60506727131777128103128289244763304935223700154879085720573969965297916}\cdot t^{66}-\frac{1402628058513691934713257515432472060721653846117188895154672327030202409517983008692035861}{121013454263554256206256578489526609870447400309758171441147939930595832}\cdot t^{64}+\frac{82868660654836616039455730926484554074853819565976780846415564734694491928152795024265904199}{60506727131777128103128289244763304935223700154879085720573969965297916}\cdot t^{62}-\frac{16294133399145426686541188171674816102690875213016879921932918230383306996664735391539317951437}{121013454263554256206256578489526609870447400309758171441147939930595832}\cdot t^{60}+\frac{2692897241413351160391826457947367119147227100061921381006385812391491950474644077077051895128905}{242026908527108512412513156979053219740894800619516342882295879861191664}\cdot t^{58}-\frac{376938812903000922079233759644517068737093714567200387526846501230616368405712797642867689093607135}{484053817054217024825026313958106439481789601239032685764591759722383328}\cdot t^{56}+\frac{44943001246331884612076463797256689437167910775786091384833761866788282392719151711784150073098818665}{968107634108434049650052627916212878963579202478065371529183519444766656}\cdot t^{54}-\frac{4583612331309798954177952140036837350817114024100498380584117365349340472724527877549133031487421278715}{1936215268216868099300105255832425757927158404956130743058367038889533312}\cdot t^{52}+\frac{401031249739100018333624952379468903833255462964189478063986446703276425729885739727344957873910838007695}{3872430536433736198600210511664851515854316809912261486116734077779066624}\cdot t^{50}-\frac{30156425734218671253568178641270292651265889287463545783382018352038827736118094963911938342432168197524625}{7744861072867472397200421023329703031708633619824522972233468155558133248}\cdot t^{48}+\frac{3901591598295350389314136417557656612674084354174001397958540804305517952008966752584417052890840954888426625}{30979444291469889588801684093318812126834534479298091888933872622232532992}\cdot t^{46}-\frac{217135788488782063920739861738676658280759041129769469604190983777946487513887099665478774987221293079879730875}{61958888582939779177603368186637624253669068958596183777867745244465065984}\cdot t^{44}+\frac{10388567908816492776595959803832021525603417410444337451783033428241199525178730723752397278040228211295100113375}{123917777165879558355206736373275248507338137917192367555735490488930131968}\cdot t^{42}-\frac{426628822961040790081598675739449657385496849908654582932857191632941540211318712753463295773372783375354864247625}{247835554331759116710413472746550497014676275834384735111470980977860263936}\cdot t^{40}+\frac{15003995448040797104547541791142235338988168703805435498240789033906079182436928484171209541528570471668797715766875}{495671108663518233420826945493100994029352551668769470222941961955720527872}\cdot t^{38}-\frac{450465466167856593974565482220471059057920050658352401658858044977264867119497185353742669800125941633574933880030625}{991342217327036466841653890986201988058705103337538940445883923911441055744}\cdot t^{36}+\frac{11499246010608790457146432684253445882628748903312891644075061432809259782830771343268741528921919272683405588590988125}{1982684434654072933683307781972403976117410206675077880891767847822882111488}\cdot t^{34}-\frac{248353114168428098765800349110881964491255206559102035774176958792531469460812577249674767719342518943789075426147981875}{3965368869308145867366615563944807952234820413350155761783535695645764222976}\cdot t^{32}+\frac{2255300119251599715762164390444193978103409048202827972272065565110432830805284930559977276286088038111570047235309586875}{3965368869308145867366615563944807952234820413350155761783535695645764222976}\cdot t^{30}-\frac{34195589779391447561266835597244138732146203403842073002803574473565199746204772584954625279146109080412616929900594315625}{7930737738616291734733231127889615904469640826700311523567071391291528445952}\cdot t^{28}+\frac{429088052668990433027008843380685446591462847888593260294855271024963302726965473104965124037292140726496549706612738803125}{15861475477232583469466462255779231808939281653400623047134142782583056891904}\cdot t^{26}-\frac{4409550575320821246361576780207483400306504382959723915299670056374324034851673535244359791641647001734371200594721244221875}{31722950954465166938932924511558463617878563306801246094268285565166113783808}\cdot t^{24}+\frac{36649188253903890239073295035637733518626221531187286915410068542940661836432868610338782341322468456401421657049557104378125}{63445901908930333877865849023116927235757126613602492188536571130332227567616}\cdot t^{22}-\frac{242649512304877429436682638727307488606043136907865840559147916040485299752337058726292190821419381443129487480972864485634375}{126891803817860667755731698046233854471514253227204984377073142260664455135232}\cdot t^{20}+\frac{1256438720010512157037922095679466618086185580776388084789388027114309043794132519971344620751791604552754311482828181496296875}{253783607635721335511463396092467708943028506454409968754146284521328910270464}\cdot t^{18}-\frac{4974295456938196079816520367567621328660441041479553899702081863782903516938513668971724565637664016923253925841809056564703125}{507567215271442671022926792184935417886057012908819937508292569042657820540928}\cdot t^{16}+\frac{58563620532509702161294659287261884995056920134657281252796212675599563596994945703209840283154413404455254597612651277562984375}{4060537722171541368183414337479483343088456103270559500066340552341262564327424}\cdot t^{14}-\frac{123717427435196206720736425766768180841228205968941711644744191787259327482692291214139560755005336917304324755854026042036578125}{8121075444343082736366828674958966686176912206541119000132681104682525128654848}\cdot t^{12}+\frac{179415894672347848486412615718668141956032659751963690818214745327273874083999283021760832325869698735122662026786125976338015625}{16242150888686165472733657349917933372353824413082238000265362209365050257309696}\cdot t^{10}-\frac{168767000218262927203256816915510183522993923513517498791038583227619243726182352656459937787965555498756319565324840470660859375}{32484301777372330945467314699835866744707648826164476000530724418730100514619392}\cdot t^8+\frac{95699342297813568316065434488226196534213183274183668897576673646126680183340127333120426777556187307673782137351516074324453125}{64968603554744661890934629399671733489415297652328952001061448837460201029238784}\cdot t^6-\frac{29482805833719617551490410694793095947980968125529946080481650838327978083619260333533347764845391011234836264763262068014609375}{129937207109489323781869258799343466978830595304657904002122897674920402058477568}\cdot t^4+\frac{3990338748311526847925265572543984127828833523129145378824877951497565302291150560556820787058640629675264683371381244791171875}{259874414218978647563738517598686933957661190609315808004245795349840804116955136}\cdot t^2-\frac{105931374000145459089288502866810388406935141037172581228151445622090277161510324657626634540729704566117844302618630775078125}{519748828437957295127477035197373867915322381218631616008491590699681608233910272}$

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.