Rule: Q[3, 4, 8]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^7-\frac{77}{18}\cdot t^5+\frac{3745}{1782}\cdot t^3-\frac{155}{594}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{15}-\frac{646576627207}{65912582718}\cdot t^{13}+\frac{1719421754504545}{110930876714394}\cdot t^{11}-\frac{36142899049575851}{2874118169418390}\cdot t^9+\frac{1577324700316391}{285731046082530}\cdot t^7-\frac{3801532399394821}{3016049930871150}\cdot t^5+\frac{2102662882898711}{16286669626704210}\cdot t^3-\frac{233879228435939}{59717788631248770}\cdot t$

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.