Rule: Q[1, 4, 18]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_3$:
  $t^{23}-\frac{154028215}{706483}\cdot t^{21}+\frac{97087532397}{4945381}\cdot t^{19}-\frac{4731252474717}{4945381}\cdot t^{17}+\frac{137523249357426}{4945381}\cdot t^{15}-\frac{354412900309590}{706483}\cdot t^{13}+\frac{4005523718729910}{706483}\cdot t^{11}-\frac{27954730328291910}{706483}\cdot t^9+\frac{115420594516104735}{706483}\cdot t^7-\frac{257825863066755555}{706483}\cdot t^5+\frac{259058096034598575}{706483}\cdot t^3-\frac{74457659847574575}{706483}\cdot t$

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.