Rule: Q[2, 58]

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^{60}-\frac{7100056248952808251326215218100848843}{2031870062999831360924751535500812}\cdot t^{58}+\frac{5791527230493455445334986465437072379759}{4063740125999662721849503071001624}\cdot t^{56}-\frac{209544792278338545268124721947505750328545}{580534303714237531692786153000232}\cdot t^{54}+\frac{73958940429153327335161553593069567418585265}{1161068607428475063385572306000464}\cdot t^{52}-\frac{38694393945555743669385549187155812489343638235}{4644274429713900253542289224001856}\cdot t^{50}+\frac{7791197202028914847874454612828453310723387265775}{9288548859427800507084578448003712}\cdot t^{48}-\frac{309486498646990861776617058169250251882004349502425}{4644274429713900253542289224001856}\cdot t^{46}+\frac{39472189964977110901679716161182062178025142554078375}{9288548859427800507084578448003712}\cdot t^{44}-\frac{16357207867757684885206703110642059944799959947622830125}{74308390875422404056676627584029696}\cdot t^{42}+\frac{1387807392178377928695548102693462423100128802484999751625}{148616781750844808113353255168059392}\cdot t^{40}-\frac{48475552991609043965651966940786450830151146441552072136375}{148616781750844808113353255168059392}\cdot t^{38}+\frac{2797179923141512100472082555990429212104206947634333073925375}{297233563501689616226706510336118784}\cdot t^{36}-\frac{266974650941614531758849853950902288190384202573488703195801875}{1188934254006758464906826041344475136}\cdot t^{34}+\frac{10532294825069122620301580737365197707016287119407151363621294375}{2377868508013516929813652082688950272}\cdot t^{32}-\frac{42848340510803620120034421618789046816868243358951098536619934375}{594467127003379232453413020672237568}\cdot t^{30}+\frac{573155942153902094785240770080120164170627733799793674220882988125}{594467127003379232453413020672237568}\cdot t^{28}-\frac{200595174188110594726684845970611295397593555310949395128681924689375}{19022948064108135438509216661511602176}\cdot t^{26}+\frac{3562030571506248739281040164397943200815761152382733235697279955421875}{38045896128216270877018433323023204352}\cdot t^{24}-\frac{25437059406158723869170737412125921704884884354799234922288603790109375}{38045896128216270877018433323023204352}\cdot t^{22}+\frac{288779202391539686349420354323588703604933370659923458053398614870109375}{76091792256432541754036866646046408704}\cdot t^{20}-\frac{5134711432568548693512814418290797351286171631825142192698012631737765625}{304367169025730167016147466584185634816}\cdot t^{18}+\frac{35077993157232416753588844267452849679164746181689207530417388967529703125}{608734338051460334032294933168371269632}\cdot t^{16}-\frac{44930089905251287769789439235341900660264697963937453113966552287476015625}{304367169025730167016147466584185634816}\cdot t^{14}+\frac{167236295333582233454784506864121225615485993842446815538087891293511796875}{608734338051460334032294933168371269632}\cdot t^{12}-\frac{1733029757638995208262679637987150582562065683476421121481195510528429484375}{4869874704411682672258359465346970157056}\cdot t^{10}+\frac{2942384255576588130997214221423582539157960278421045161138778077110840296875}{9739749408823365344516718930693940314112}\cdot t^8-\frac{1496078334397705381994991141402369261385888464530449531019768188751825015625}{9739749408823365344516718930693940314112}\cdot t^6+\frac{785612112686584460193819891583289376321955023546619889268345022084261640625}{19479498817646730689033437861387880628224}\cdot t^4-\frac{318518767898765749373335667107812800294204251487497105917203917321792265625}{77917995270586922756133751445551522512896}\cdot t^2+\frac{10398555386079770047503022980751344714023432533006199393077801080060703125}{155835990541173845512267502891103045025792}$

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.