Rule: Q[8, 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.

• $P_1$:
  $\frac{1}{40320}\cdot t^8-\frac{1}{630}\cdot t^7+\frac{7}{180}\cdot t^6-\frac{7}{15}\cdot t^5+\frac{35}{12}\cdot t^4-\frac{28}{3}\cdot t^3+14\cdot t^2-8\cdot t+1$
• $P_2$:
  $\frac{1}{40320}\cdot t^{21}-\frac{175357873392868770223885121}{22322221904830692598108333440}\cdot t^{20}+\frac{13093342200490858587597836363}{11719166500036113614006875056}\cdot t^{19}-\frac{229123320966736111039489489829}{2421315392569444961571668400}\cdot t^{18}+\frac{173781018111036721952037276070659}{32553240277878093372241319600}\cdot t^{17}-\frac{141240791513961633754320962798007}{664351842405675374943700400}\cdot t^{16}+\frac{12576919914229524848470685376423941}{2034577517367380835765082475}\cdot t^{15}-\frac{10896821990380721247284594781280395}{81383100694695233430603299}\cdot t^{14}+\frac{355728382234134044192427972043903963}{162766201389390466861206598}\cdot t^{13}-\frac{4398758476168286079084527583127419427}{162766201389390466861206598}\cdot t^{12}+\frac{20609168997115831850083934139850522452}{81383100694695233430603299}\cdot t^{11}-\frac{1204337321595714022552619230557322524}{672587609047068044881019}\cdot t^{10}+\frac{70067770935634382515034464841319527820}{7398463699517748493691209}\cdot t^9-\frac{273403384856197720167659823480675832092}{7398463699517748493691209}\cdot t^8+\frac{70139033187444363620773201421643118848}{672587609047068044881019}\cdot t^7-\frac{218754865742839604980918183884199788288}{1056923385645392641955887}\cdot t^6+\frac{293661005406952226646725146300287675456}{1056923385645392641955887}\cdot t^5-\frac{252128554210467865785809206521588571200}{1056923385645392641955887}\cdot t^4+\frac{127360767357113109689832974775572590080}{1056923385645392641955887}\cdot t^3-\frac{33151322444018766236297256903869790720}{1056923385645392641955887}\cdot t^2+\frac{3529869979421388132487784994808343040}{1056923385645392641955887}\cdot t-\frac{93822572514457738289078395490234880}{1056923385645392641955887}$

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.