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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^9-36\cdot t^7+189\cdot t^5-315\cdot t^3+\frac{945}{8}\cdot t$
• $P_3$:
  $2\cdot t^{25}-\frac{23762980}{100507}\cdot t^{23}+\frac{5852078041}{502535}\cdot t^{21}-\frac{157472863947}{502535}\cdot t^{19}+\frac{20424353912697}{4020280}\cdot t^{17}-\frac{51928112026581}{1005070}\cdot t^{15}+\frac{267845732796915}{804056}\cdot t^{13}-\frac{98477176545657}{73096}\cdot t^{11}+\frac{3873311363563551}{1169536}\cdot t^9-\frac{2729715557905791}{584768}\cdot t^7+\frac{7966597330394703}{2339072}\cdot t^5-\frac{2482191962093025}{2339072}\cdot t^3+\frac{1679491299241665}{18712576}\cdot t$

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.