Rule: Q[5, 9]

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.

• $P_1$:
  $\frac{-1}{120}\cdot t^5+\frac{5}{24}\cdot t^4-\frac{5}{3}\cdot t^3+5\cdot t^2-5\cdot t+1$
• $P_2$:
  $\frac{-1}{120}\cdot t^{14}+\frac{630035846581}{524291592864}\cdot t^{13}-\frac{14842226222329}{201650612640}\cdot t^{12}+\frac{21179159056139}{8402108860}\cdot t^{11}-\frac{1168706186031505}{21845483036}\cdot t^{10}+\frac{80556020627567989}{109227415180}\cdot t^9-\frac{735639626017132389}{109227415180}\cdot t^8+\frac{1114897981156484472}{27306853795}\cdot t^7-\frac{4431253781369574936}{27306853795}\cdot t^6+\frac{11231306886060577764}{27306853795}\cdot t^5-\frac{3461630624570887524}{5461370759}\cdot t^4+\frac{2996233735138195104}{5461370759}\cdot t^3-\frac{1262784321733279968}{5461370759}\cdot t^2+\frac{188646488106892704}{5461370759}\cdot t-\frac{2731807459122336}{5461370759}$

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.