Rule: Q[4, 13]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{17}-\frac{20554887}{1192364}\cdot t^{15}+\frac{16554685}{596182}\cdot t^{13}-\frac{43561973}{1850220}\cdot t^{11}+\frac{927511585}{82273116}\cdot t^9-\frac{83298215}{27424372}\cdot t^7+\frac{1686197513}{3907973010}\cdot t^5-\frac{14357343}{521063068}\cdot t^3+\frac{2723149}{5210630680}\cdot t$

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.