Rule: Q[4, 54]

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^{58}-\frac{1927247844876430567926952406969296728032807680584}{156076154376443784020471091257586920927888413}\cdot t^{56}+\frac{17279266019006778662638474953980504516346736311907584}{3901903859411094600511777281439673023197210325}\cdot t^{54}-\frac{3828889861624268390184819835878807951217135362558191352}{3901903859411094600511777281439673023197210325}\cdot t^{52}+\frac{34587858134481660284478592287171583651388751293211735489}{229523756435946741206575134202333707246894725}\cdot t^{50}-\frac{313103327864853580056994855510085933893495397465880034137}{18361900514875739296526010736186696579751578}\cdot t^{48}+\frac{13549036893792942307005253964464767077217346848673562347746}{9180950257437869648263005368093348289875789}\cdot t^{46}-\frac{918984551499850730722192022466531110134736288657100004429986}{9180950257437869648263005368093348289875789}\cdot t^{44}+\frac{794538845014129648470699268513392214962153278336572792544979633}{146895204119005914372208085889493572638012624}\cdot t^{42}-\frac{69177487823800388923668858675473939865661041605149032198053267109}{293790408238011828744416171778987145276025248}\cdot t^{40}+\frac{611018162814638624734923768212064396310093864334979262613006496555}{73447602059502957186104042944746786319006312}\cdot t^{38}-\frac{70391911151115054771335792282248412102736027506400928801723763476995}{293790408238011828744416171778987145276025248}\cdot t^{36}+\frac{779333637989924765643210269685418935211618979283419582967216903376845}{138254309759064389997372316131288068365188352}\cdot t^{34}-\frac{29953719089485537915319425979961383177602128725119829198718300016537845}{276508619518128779994744632262576136730376704}\cdot t^{32}+\frac{1892266351813845756512592142054480065040049169038662731934798533831435}{1114954110960196693527196097832968293267648}\cdot t^{30}-\frac{3009432720079112753655048444871701110210837956184619529189167055982325}{139369263870024586690899512229121036658456}\cdot t^{28}+\frac{15827838074432466441339204342458276552820853695777100397796891393111866025}{71357063101452588385740550261309970769129472}\cdot t^{26}-\frac{260447175123455310528954174062809760942587897966400013532752871124826895125}{142714126202905176771481100522619941538258944}\cdot t^{24}+\frac{3609087898174067165036330955440198293331153799181040284355460164140920284625}{303267518181173500639397338610567375768800256}\cdot t^{22}-\frac{147237944811654950859198984232732669658481526220615165148338022124266693439875}{2426140145449388005115178708884539006150402048}\cdot t^{20}+\frac{16670128167846588697048695682599561283528776789042767862362650047380160020625}{70069029471462469461810215419048057939361792}\cdot t^{18}-\frac{1601719386333225827265394935155227513552067890041845876657879164516684547563125}{2283426019246482828343697608361919064612143104}\cdot t^{16}+\frac{863240581079694267738270730915967127839910306325838177518432832035523339566875}{570856504811620707085924402090479766153035776}\cdot t^{14}-\frac{1311159053249787030432329686074592697628660004794526232725541538969612634100625}{570856504811620707085924402090479766153035776}\cdot t^{12}+\frac{42713170349850561155381000153393496356203614985665963913784416637898486396283125}{18267408153971862626749580866895352516897144832}\cdot t^{10}-\frac{54370761792643034557102493761731183274925589864972879043430856425611512784715625}{36534816307943725253499161733790705033794289664}\cdot t^8+\frac{4887206491208354686489118099189132270659035526237353219116101254423696673940625}{9133704076985931313374790433447676258448572416}\cdot t^6-\frac{3393251311775997349379287530126235887554224439059568110763834623713159001044375}{36534816307943725253499161733790705033794289664}\cdot t^4+\frac{1732666741636409132971923115171010390371477989116234686321365942463579342580625}{292278530463549802027993293870325640270354317312}\cdot t^2-\frac{38861352563804617800545142221247228372176854072008492018589507033117973735625}{584557060927099604055986587740651280540708634624}$

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.