Rule: Q[3, 10]

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.

• $P_1$:
  $\frac{-1}{6}\cdot t^3+\frac{3}{2}\cdot t^2-3\cdot t+1$
• $P_2$:
  $\frac{-1}{6}\cdot t^{13}+\frac{421712143933}{18158932572}\cdot t^{12}-\frac{16580419893369}{12105955048}\cdot t^{11}+\frac{3812509465873861}{84741685336}\cdot t^{10}-\frac{38643094608812075}{42370842668}\cdot t^9+\frac{506353552676384715}{42370842668}\cdot t^8-\frac{1091984068621849140}{10592710667}\cdot t^7+\frac{885051068496082740}{1513244381}\cdot t^6-\frac{3240102316652961480}{1513244381}\cdot t^5+\frac{7343058389706333000}{1513244381}\cdot t^4-\frac{9557249357291194800}{1513244381}\cdot t^3+\frac{6247991847912253200}{1513244381}\cdot t^2-\frac{1581098381678210400}{1513244381}\cdot t+\frac{80788952144584800}{1513244381}$

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.