Rule: Q[3, 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.

• $P_1$:
  $\frac{-1}{6}\cdot t^3+\frac{3}{2}\cdot t^2-3\cdot t+1$
• $P_2$:
  $\frac{-1}{6}\cdot t^{11}+\frac{278027299}{14518338}\cdot t^{10}-\frac{6456647635}{7259169}\cdot t^9+\frac{263868946087}{12098615}\cdot t^8-\frac{3742703600368}{12098615}\cdot t^7+\frac{31654483962416}{12098615}\cdot t^6-\frac{158924768527392}{12098615}\cdot t^5+\frac{91552595564640}{2419723}\cdot t^4-\frac{141117953419968}{2419723}\cdot t^3+\frac{102658053097152}{2419723}\cdot t^2-\frac{27723949110144}{2419723}\cdot t+\frac{1551192547968}{2419723}$

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.