Rule: Q[2, 6, 7]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{15}-\frac{52675}{9724}\cdot t^{13}+\frac{62424565}{7972932}\cdot t^{11}-\frac{25786918405}{4472814852}\cdot t^9+\frac{30491079041}{13418444556}\cdot t^7-\frac{701814715}{1530173502}\cdot t^5+\frac{12997042835}{319806261918}\cdot t^3-\frac{1504480675}{1439128178631}\cdot t$

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.