Rule: Q[4, 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.

• $P_1$:
  $\frac{1}{24}\cdot t^4-\frac{2}{3}\cdot t^3+3\cdot t^2-4\cdot t+1$
• $P_2$:
  $\frac{1}{24}\cdot t^{12}-\frac{381335062}{82729245}\cdot t^{11}+\frac{87230680367}{413646225}\cdot t^{10}-\frac{2160818771668}{413646225}\cdot t^9+\frac{2126466325051}{27576415}\cdot t^8-\frac{97112179256768}{137882075}\cdot t^7+\frac{552615268232608}{137882075}\cdot t^6-\frac{1927933730986368}{137882075}\cdot t^5+\frac{792526186186224}{27576415}\cdot t^4-\frac{178548847169280}{5515283}\cdot t^3+\frac{484872023567232}{27576415}\cdot t^2-\frac{99066799544832}{27576415}\cdot t+\frac{4117291581312}{27576415}$

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.