Rule: Q[8, 9]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{17}-\frac{517803}{2432}\cdot t^{15}+\frac{1876545}{5054}\cdot t^{13}-\frac{6070696515}{17668784}\cdot t^{11}+\frac{1702074702185}{9399793088}\cdot t^9-\frac{145391570181}{2685655168}\cdot t^7+\frac{5762999385}{671413792}\cdot t^5-\frac{820541865}{1342827584}\cdot t^3+\frac{34073955}{2685655168}\cdot t$

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.