Rule: Q[6, 12]

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.

• $P_1$:
  $\frac{1}{720}\cdot t^6-\frac{1}{20}\cdot t^5+\frac{5}{8}\cdot t^4-\frac{10}{3}\cdot t^3+\frac{15}{2}\cdot t^2-6\cdot t+1$
• $P_2$:
  $\frac{1}{720}\cdot t^{18}-\frac{33255221371886127}{34757756461623743}\cdot t^{17}+\frac{30206384193517003044}{173788782308118715}\cdot t^{16}-\frac{2720969863800472808106}{173788782308118715}\cdot t^{15}+\frac{1647820089272647841418825}{1946434361850929608}\cdot t^{14}-\frac{14591505802007837764750035}{486608590462732402}\cdot t^{13}+\frac{709035899712122762576965375}{973217180925464804}\cdot t^{12}-\frac{432627251105229480605887380}{34757756461623743}\cdot t^{11}+\frac{36809819304179340538843285815}{243304295231366201}\cdot t^{10}-\frac{319018397664033381317200167300}{243304295231366201}\cdot t^9+\frac{1959762976637263014431268926190}{243304295231366201}\cdot t^8-\frac{8415003011924259306782280489600}{243304295231366201}\cdot t^7+\frac{3524939371049709342680351177040}{34757756461623743}\cdot t^6-\frac{6812221008259057617687822989760}{34757756461623743}\cdot t^5+\frac{8226488246661538240805174988000}{34757756461623743}\cdot t^4-\frac{5712070601711490893770079577600}{34757756461623743}\cdot t^3+\frac{1975871799779310464027424912000}{34757756461623743}\cdot t^2-\frac{251705839963395060009627379200}{34757756461623743}\cdot t+\frac{4237901511990657331621996800}{34757756461623743}$

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.