Rule: Q[2, 20]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{22}-\frac{30461783}{3830466}\cdot t^{20}+\frac{66155815}{3643614}\cdot t^{18}-\frac{14341808855}{614151382}\cdot t^{16}+\frac{39940250075}{2149529837}\cdot t^{14}-\frac{670092247}{70863621}\cdot t^{12}+\frac{2251326473}{732257417}\cdot t^{10}-\frac{13150594545}{21235465093}\cdot t^8+\frac{27599544115}{382238371674}\cdot t^6-\frac{544763725}{127412790558}\cdot t^4+\frac{4285838227}{43957412742510}\cdot t^2-\frac{333527539}{923105667592710}$

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.