Rule: Q[2, 33]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{35}-\frac{2309140361065}{179257449842}\cdot t^{33}+\frac{58882849375020}{1165173423973}\cdot t^{31}-\frac{31557996232180}{263103676381}\cdot t^{29}+\frac{1322543478970010}{6878281825389}\cdot t^{27}-\frac{2290165419312342}{10405605838409}\cdot t^{25}+\frac{1929607523226900}{10405605838409}\cdot t^{23}-\frac{23102292320873700}{197706510929771}\cdot t^{21}+\frac{580441481108252775}{10478445079277863}\cdot t^{19}-\frac{184263140177325}{9347408634503}\cdot t^{17}+\frac{140921092394370420}{27023358362348173}\cdot t^{15}-\frac{3447412721538300}{3423444320836561}\cdot t^{13}+\frac{25026534359773050}{181442549004337733}\cdot t^{11}-\frac{100105115452187450}{7802029607186522519}\cdot t^9+\frac{242559615554378100}{319883213894647423279}\cdot t^7-\frac{106262835974794620}{4158481780630416502627}\cdot t^5+\frac{124163980863599325}{307727651766650821194398}\cdot t^3-\frac{4076450003248425}{2154093562366555748360786}\cdot t$

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.