Rule: Q[2, 4, 36]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{42}-\frac{199097463822235860028643931918410178917}{12929578683859425743227577424470076064}\cdot t^{40}+\frac{285168766138679841058016877413435263629993}{3891803183841687148711500804765492895264}\cdot t^{38}-\frac{304671812314423622561850018765914721305009407}{1420508162102215809279697793739404906771360}\cdot t^{36}+\frac{1245323226447397677224846957535154221780032151}{2881602271693066355967386953014221382307616}\cdot t^{34}-\frac{52030534748248406768204207774768181046329699}{81863700900371203294528038437904016542830}\cdot t^{32}+\frac{356193372574226986280549317838652806833465748907}{504607852349888097107470828931240357970004120}\cdot t^{30}-\frac{8711588189574063399080895728172281920058913303}{14417367209996802774499166540892581656285832}\cdot t^{28}+\frac{203530799064527956543660477693314045551437480713}{504607852349888097107470828931240357970004120}\cdot t^{26}-\frac{18191993962824867302090051236013671374593786732955}{86187021181360886985956017581455853141276703696}\cdot t^{24}+\frac{1740723583981711871284567190644097718512975062221}{20098949603558467716092510028877056661404448688}\cdot t^{22}-\frac{79633272368646510739664209419305731625545406841}{2871278514794066816584644289839579523057778384}\cdot t^{20}+\frac{2385359982076467299385436521906554548040339111805}{347424700290082084806741959070589122289991184464}\cdot t^{18}-\frac{11916307863985703593806674880243511512292700294367}{9206754557687175247378661915370611740684766388296}\cdot t^{16}+\frac{3919116539774835467194251923117771177998013895}{21561486083576522827584688326394875270924511448}\cdot t^{14}-\frac{1187840417845019403331212243302111408942689417293}{64447281903810226731650633407594282184793364718072}\cdot t^{12}+\frac{52924237421978584821959969414937454269701866737}{41011906666061053374686766713923634117595777547864}\cdot t^{10}-\frac{9579703795327944478307465874877493396026364355}{164047626664244213498747066855694536470383110191456}\cdot t^8+\frac{72927842206065407039660456955411453421210820049}{47362893355491079354423974587908379743806323670990368}\cdot t^6-\frac{935719971358212080914766762202420706098236835}{47362893355491079354423974587908379743806323670990368}\cdot t^4+\frac{3994727003890353065099015874438473085328647}{47362893355491079354423974587908379743806323670990368}\cdot t^2-\frac{4929916250893266608172739693442608503}{153775627777568439462415501908793440726643908022696}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.