Rule: Q[2, 4, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{13}-\frac{11979409}{2770390}\cdot t^{11}+\frac{54031549}{11635638}\cdot t^9-\frac{751494029}{329676410}\cdot t^7+\frac{11821062}{23548315}\cdot t^5-\frac{193274}{4709663}\cdot t^3+\frac{52009}{70644945}\cdot t$

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.