Rule: Q[4, 18]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{22}-\frac{4464152121}{191548568}\cdot t^{20}+\frac{113408704076613}{2119101807784}\cdot t^{18}-\frac{5141152044847599}{74168563272440}\cdot t^{16}+\frac{412630972878933}{7416856327244}\cdot t^{14}-\frac{72312906879441}{2526621386204}\cdot t^{12}+\frac{691191914990115}{73272020199916}\cdot t^{10}-\frac{141675704352963}{73272020199916}\cdot t^8+\frac{844966842584733}{3663601009995800}\cdot t^6-\frac{711697261325501}{50557693937942040}\cdot t^4+\frac{39461412446203}{117967952521864760}\cdot t^2-\frac{154908650299}{117967952521864760}$

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.