Rule: Q[31]

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.

• $P_1$:
  $\frac{14544636039226909}{67108864}\cdot t^{31}-\frac{110873045217057585}{67108864}\cdot t^{29}+\frac{381478443712926945}{67108864}\cdot t^{27}-\frac{783034700252850045}{67108864}\cdot t^{25}+\frac{1067774591253886425}{67108864}\cdot t^{23}-\frac{1019422534291446285}{67108864}\cdot t^{21}+\frac{699603700003933725}{67108864}\cdot t^{19}-\frac{348782019535488825}{67108864}\cdot t^{17}+\frac{126155198555389575}{67108864}\cdot t^{15}-\frac{32706903329175075}{67108864}\cdot t^{13}+\frac{5932880138780595}{67108864}\cdot t^{11}-\frac{723521968143975}{67108864}\cdot t^9+\frac{55655536011075}{67108864}\cdot t^7-\frac{2429867476575}{67108864}\cdot t^5+\frac{49589132175}{67108864}\cdot t^3-\frac{300540195}{67108864}\cdot t$

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.