Rule: Q[7, 22]

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.

• $P_1$:
  $\frac{429}{16}\cdot t^7-\frac{693}{16}\cdot t^5+\frac{315}{16}\cdot t^3-\frac{35}{16}\cdot t$
• $P_2$:
  $\frac{429}{16}\cdot t^{29}-\frac{14066159496200785202911}{75314553958848004656}\cdot t^{27}+\frac{12794931877504112076663}{21966744904664001358}\cdot t^{25}-\frac{1923984533484479941788085825}{1792310650261345198801936}\cdot t^{23}+\frac{10480438621786097608689191575}{8065397926176053394608712}\cdot t^{21}-\frac{2242118959033464701350852120}{2064357802533156523620087}\cdot t^{19}+\frac{2432954537915015329944393665}{3793329743590338037800496}\cdot t^{17}-\frac{10719598122967893271804173295}{39829962307698549396905208}\cdot t^{15}+\frac{2113363290885989308160202725}{26553308205132366264603472}\cdot t^{13}-\frac{430582570971098884496726425}{26553308205132366264603472}\cdot t^{11}+\frac{609251634990477933822706195}{278809736153889845778336456}\cdot t^9-\frac{38792296717571643388798134765}{213196511579007768738501276688}\cdot t^7+\frac{1476486345261845966461985}{177073514600504791311047572}\cdot t^5-\frac{9939825411941202012429025}{58737814414624589346321780312}\cdot t^3+\frac{249576889875869727625225}{274109800601581416949501641456}\cdot t$

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.