Rule: Q[2, 3, 10]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{15}-\frac{61157207}{11447800}\cdot t^{13}+\frac{3237322021}{425329800}\cdot t^{11}-\frac{247214528}{44659629}\cdot t^9+\frac{215329367}{99243620}\cdot t^7-\frac{4051191133}{9158768360}\cdot t^5+\frac{5596988947}{137381525400}\cdot t^3-\frac{336966223}{297659971700}\cdot t$

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.