Rule: Q[1, 3, 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.

• $P_1$:
  $-t+1$
• $P_2$:
  $-t^4+\frac{49}{4}\cdot t^3-\frac{153}{4}\cdot t^2+\frac{57}{2}\cdot t-\frac{3}{2}$
• $P_3$:
  $-t^{11}+\frac{3392967828406597}{35581698318300}\cdot t^{10}-\frac{263171002995616061}{71163396636600}\cdot t^9+\frac{360863401741672131}{4744226442440}\cdot t^8-\frac{43090000478835438697}{47442264424400}\cdot t^7+\frac{307806075790591533337}{47442264424400}\cdot t^6-\frac{654931550855543318721}{23721132212200}\cdot t^5+\frac{321249949241386686423}{4744226442440}\cdot t^4-\frac{21206270089716845259}{237211322122}\cdot t^3+\frac{66432143812531301091}{1186056610610}\cdot t^2-\frac{7673711663467963953}{593028305305}\cdot t+\frac{338438366351142183}{593028305305}$

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.