Rule: Q[2, 12, 23]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{14}-\frac{124249}{1555}\cdot t^{12}+\frac{3530769}{1555}\cdot t^{10}-\frac{8883963}{311}\cdot t^8+\frac{50229333}{311}\cdot t^6-\frac{114812775}{311}\cdot t^4+\frac{78937551}{311}\cdot t^2-\frac{6151761}{311}$
• $P_3$:
  $t^{37}-\frac{5206884703785885069401677643109785203839199881736405351984973}{11066327465203363561144655495935600117998477897742339287660}\cdot t^{35}+\frac{2156429944282243047560762390617286453826152091146369834371071307}{22132654930406727122289310991871200235996955795484678575320}\cdot t^{33}-\frac{86671141549637352704475679652555623951611997891451497886174682427}{7377551643468909040763103663957066745332318598494892858440}\cdot t^{31}+\frac{123518601412956111184936671657539022617506177131307392658484794715885}{134271439911134144541888486684018614765048198492607050023608}\cdot t^{29}-\frac{6634894636616140976129239001203571630003689171698638172481741732529783}{134271439911134144541888486684018614765048198492607050023608}\cdot t^{27}+\frac{27984193286268544860406840523333155528054351995643712525407140010370871}{14919048879014904949098720742668734973894244276956338891512}\cdot t^{25}-\frac{762319826189697387389954799944129656121308992952344429367894845400093273}{14919048879014904949098720742668734973894244276956338891512}\cdot t^{23}+\frac{2141154568056680646228102431828154896676041637403169249211150215822469967}{2131292697002129278442674391809819281984892039565191270216}\cdot t^{21}-\frac{2332727986225237200396896324418045137505390260409204757726171557292053045}{163945592077086867572513414754601483229607079966553174632}\cdot t^{19}+\frac{306647904980060519990721883441138932051996577804641660311663146649331107295}{2131292697002129278442674391809819281984892039565191270216}\cdot t^{17}-\frac{2177945703339572817190900580135097263659178954192712199266029099102007723105}{2131292697002129278442674391809819281984892039565191270216}\cdot t^{15}+\frac{10594131628712078808649316189348036060554190415129309632821986435893666840505}{2131292697002129278442674391809819281984892039565191270216}\cdot t^{13}-\frac{2615777001630548106955338323855385492351061247026664881831433485591159869255}{163945592077086867572513414754601483229607079966553174632}\cdot t^{11}+\frac{5243227607723868206507210155028908789967102821968911098249588328935428433575}{163945592077086867572513414754601483229607079966553174632}\cdot t^9-\frac{6025327761610584106536736008289786718370542873480159816510125947967967444025}{163945592077086867572513414754601483229607079966553174632}\cdot t^7+\frac{3440106866321040850522941439207881228368189838811425201201348807406843590225}{163945592077086867572513414754601483229607079966553174632}\cdot t^5-\frac{754916267618211034491302104174238743065302564319660875949733949124139476225}{163945592077086867572513414754601483229607079966553174632}\cdot t^3+\frac{10968860114584057416273968979414201488964692856321689645227909669688919075}{40986398019271716893128353688650370807401769991638293658}\cdot t$

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.