Rule: Q[3, 7]

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.

• $P_1$:
  $\frac{-1}{6}\cdot t^3+\frac{3}{2}\cdot t^2-3\cdot t+1$
• $P_2$:
  $\frac{-1}{6}\cdot t^{10}+\frac{13125919}{971340}\cdot t^9-\frac{141392943}{323780}\cdot t^8+\frac{4724634611}{647560}\cdot t^7-\frac{44335180547}{647560}\cdot t^6+\frac{119048783931}{323780}\cdot t^5-\frac{71613183117}{64756}\cdot t^4+\frac{28343232813}{16189}\cdot t^3-\frac{20923244433}{16189}\cdot t^2+\frac{5665869846}{16189}\cdot t-\frac{309371706}{16189}$

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.