Rule: Q[1, 8, 16]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-36\cdot t^7+378\cdot t^5-1260\cdot t^3+945\cdot t$
• $P_3$:
  $t^{25}-\frac{23762980}{100507}\cdot t^{23}+\frac{11704156082}{502535}\cdot t^{21}-\frac{629891455788}{502535}\cdot t^{19}+\frac{20424353912697}{502535}\cdot t^{17}-\frac{415424896212648}{502535}\cdot t^{15}+\frac{1071382931187660}{100507}\cdot t^{13}-\frac{787817412365256}{9137}\cdot t^{11}+\frac{3873311363563551}{9137}\cdot t^9-\frac{10918862231623164}{9137}\cdot t^7+\frac{15933194660789406}{9137}\cdot t^5-\frac{9928767848372100}{9137}\cdot t^3+\frac{1679491299241665}{9137}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.