Rule: Q[7, 13]

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.

• $P_1$:
  $\frac{-1}{5040}\cdot t^7+\frac{7}{720}\cdot t^6-\frac{7}{40}\cdot t^5+\frac{35}{24}\cdot t^4-\frac{35}{6}\cdot t^3+\frac{21}{2}\cdot t^2-7\cdot t+1$
• $P_2$:
  $\frac{-1}{5040}\cdot t^{20}+\frac{99500877068637043370825957}{1421876558706119868637222560}\cdot t^{19}-\frac{15375224266994843260464236723}{1421876558706119868637222560}\cdot t^{18}+\frac{1603792293969362038671102952}{1645690461465416514626415}\cdot t^{17}-\frac{151195968834239082352704262063}{2633104738344666423402264}\cdot t^{16}+\frac{61802785901079124212858617915791}{26331047383446664234022640}\cdot t^{15}-\frac{51812766244054232665876150397455}{752315639527047549543504}\cdot t^{14}+\frac{11691158508333244832759252775750835}{7899314215033999270206792}\cdot t^{13}-\frac{186019990097246850867736139525822035}{7899314215033999270206792}\cdot t^{12}+\frac{61129148370784011837992606765489775}{219425394862055535283522}\cdot t^{11}-\frac{1610815573457098361631951842238561635}{658276184586166605850566}\cdot t^{10}+\frac{5217967953159533687656251869485946905}{329138092293083302925283}\cdot t^9-\frac{8211252714671828648604121731880365015}{109712697431027767641761}\cdot t^8+\frac{469974862693706328255686560880983560}{1859537244593690976979}\cdot t^7-\frac{9315559026635610065210610021664702200}{15673242490146823948823}\cdot t^6+\frac{14684939012313682451075285133378496560}{15673242490146823948823}\cdot t^5-\frac{14684214920740026942035682533926004400}{15673242490146823948823}\cdot t^4+\frac{8582849228779052447900425448767521600}{15673242490146823948823}\cdot t^3-\frac{2593330654780898434586820682235217600}{15673242490146823948823}\cdot t^2+\frac{338248593053810606177694047933712000}{15673242490146823948823}\cdot t-\frac{13498080248464191937306955985436800}{15673242490146823948823}$

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.