Rule: Q[4, 11]

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.

• $P_1$:
  $\frac{1}{24}\cdot t^4-\frac{2}{3}\cdot t^3+3\cdot t^2-4\cdot t+1$
• $P_2$:
  $\frac{1}{24}\cdot t^{15}-\frac{2582685385518509}{342153039075864}\cdot t^{14}+\frac{50572983713511755}{85538259768966}\cdot t^{13}-\frac{1130462181125218829}{42769129884483}\cdot t^{12}+\frac{74864723642114561651}{99794636397127}\cdot t^{11}-\frac{1420042046675839732871}{99794636397127}\cdot t^{10}+\frac{18460663150990015998460}{99794636397127}\cdot t^9-\frac{165990490853443547940000}{99794636397127}\cdot t^8+\frac{1028856920195827994586480}{99794636397127}\cdot t^7-\frac{618309799772068099135440}{14256376628161}\cdot t^6+\frac{1713014779541963586575040}{14256376628161}\cdot t^5-\frac{2972690419430647704412800}{14256376628161}\cdot t^4+\frac{2979133428781164249936000}{14256376628161}\cdot t^3-\frac{1504412072863215900278400}{14256376628161}\cdot t^2+\frac{296735875510868927654400}{14256376628161}\cdot t-\frac{12326755351750243430400}{14256376628161}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.