Rule: Q[5, 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.

• $P_1$:
  $\frac{-1}{120}\cdot t^5+\frac{5}{24}\cdot t^4-\frac{5}{3}\cdot t^3+5\cdot t^2-5\cdot t+1$
• $P_2$:
  $\frac{-1}{120}\cdot t^{15}+\frac{24125925455475}{15985778765768}\cdot t^{14}-\frac{2818735843365475}{23978668148652}\cdot t^{13}+\frac{124484157226526725}{23978668148652}\cdot t^{12}-\frac{41206882302314925}{285460335103}\cdot t^{11}+\frac{5305308441249004355}{1998222345721}\cdot t^{10}-\frac{9434069728320909050}{285460335103}\cdot t^9+\frac{80001919404519681150}{285460335103}\cdot t^8-\frac{3216417224803558592400}{1998222345721}\cdot t^7+\frac{1756047719368892689200}{285460335103}\cdot t^6-\frac{4327553496492192834720}{285460335103}\cdot t^5+\frac{6540269333634064476000}{285460335103}\cdot t^4-\frac{5598638202813663888000}{285460335103}\cdot t^3+\frac{2382225603316738704000}{285460335103}\cdot t^2-\frac{398982808635302304000}{285460335103}\cdot t+\frac{15571971090317433600}{285460335103}$

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.