Rule: Q[5, 16]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{21}-\frac{123674670581}{3171265708}\cdot t^{19}+\frac{180709480704313}{2188173338520}\cdot t^{17}-\frac{12083075931599}{123646781115}\cdot t^{15}+\frac{6071112915091}{85667865492}\cdot t^{13}-\frac{73112519652907}{2249360306094}\cdot t^{11}+\frac{132291375506969}{14088469879548}\cdot t^9-\frac{467353268908967}{283726129518675}\cdot t^7+\frac{8441023069733807}{52205607831436200}\cdot t^5-\frac{117288300587981}{15661682349430860}\cdot t^3+\frac{1112587844447}{10441121566287240}\cdot t$

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.