Rule: Q[8, 22]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{30}-\frac{805612412622208}{18480916529}\cdot t^{28}+\frac{58920743374080768}{18480916529}\cdot t^{26}-\frac{2440819600664020800}{18480916529}\cdot t^{24}+\frac{63620982302650892400}{18480916529}\cdot t^{22}-\frac{1096825683184185616200}{18480916529}\cdot t^{20}+\frac{753209077581214115400}{1087112737}\cdot t^{18}-\frac{5996966544476638592400}{1087112737}\cdot t^{16}+\frac{32370599322094287783375}{1087112737}\cdot t^{14}-\frac{232354608261896447452125}{2174225474}\cdot t^{12}+\frac{3763571335948745070750}{15311447}\cdot t^{10}-\frac{1479484787563701162869625}{4348450948}\cdot t^8+\frac{4427866251098037244121625}{17393803792}\cdot t^6-\frac{2944702489166228915499375}{34787607584}\cdot t^4+\frac{284137896676777816798125}{34787607584}\cdot t^2-\frac{1526335156436577361875}{34787607584}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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