Rule: Q[2, 4, 7]

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.

• $P_1$:
  $\frac{1}{2}\cdot t^2-2\cdot t+1$
• $P_2$:
  $\frac{1}{2}\cdot t^6-\frac{162}{13}\cdot t^5+101\cdot t^4-\frac{4208}{13}\cdot t^3+\frac{5436}{13}\cdot t^2-\frac{2928}{13}\cdot t+\frac{552}{13}$
• $P_3$:
  $\frac{1}{2}\cdot t^{13}-\frac{504112280487697156627091}{9075455013440231194662}\cdot t^{12}+\frac{998316189656555410719133}{387839957839326119430}\cdot t^{11}-\frac{2965739118746776745361636253}{45377275067201155973310}\cdot t^{10}+\frac{45607911258484289158420733437}{45377275067201155973310}\cdot t^9-\frac{49287488556967664430621524593}{5041919451911239552590}\cdot t^8+\frac{922918877240621604852845252953}{15125758355733718657770}\cdot t^7-\frac{3679124253775711321498662080329}{15125758355733718657770}\cdot t^6+\frac{509555203104173268417633885977}{840319908651873258765}\cdot t^5-\frac{459720959095965190437388662941}{504191945191123955259}\cdot t^4+\frac{396084508837739379956824010996}{504191945191123955259}\cdot t^3-\frac{20165652924904405596774307428}{56021327243458217251}\cdot t^2+\frac{12744533040892287406126521992}{168063981730374651753}\cdot t-\frac{800328217570399243256211128}{168063981730374651753}$

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.