Rule: Q[1, 6, 8]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{21}{13}\cdot t^5+\frac{105}{143}\cdot t^3-\frac{35}{429}\cdot t$
• $P_3$:
  $t^{15}-\frac{825}{221}\cdot t^{13}+\frac{336705}{60401}\cdot t^{11}-\frac{8310395}{1960287}\cdot t^9+\frac{8381629155}{4854324041}\cdot t^7-\frac{250360401}{693474863}\cdot t^5+\frac{300170185}{9015173219}\cdot t^3-\frac{88221135}{99166905409}\cdot t$

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.