Rule: Q[2, 4, 9]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{15}-\frac{1280116003}{245021714}\cdot t^{13}+\frac{12427268373}{1715151998}\cdot t^{11}-\frac{61055366515}{12006063986}\cdot t^9+\frac{7331508745275}{3877958667478}\cdot t^7-\frac{195050681397}{553994095354}\cdot t^5+\frac{14996878941}{553994095354}\cdot t^3-\frac{264841293}{553994095354}\cdot t$

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.