Rule: Q[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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{24}-\frac{5424530944}{205799}\cdot t^{22}+\frac{1144816116864}{1028995}\cdot t^{20}-\frac{25882957659776}{1028995}\cdot t^{18}+\frac{68809147521296}{205799}\cdot t^{16}-\frac{556247611045056}{205799}\cdot t^{14}+\frac{2738586270109872}{205799}\cdot t^{12}-\frac{728436514142064}{18709}\cdot t^{10}+\frac{1200200825947851}{18709}\cdot t^8-\frac{1009122581859210}{18709}\cdot t^6+\frac{719728821634095}{37418}\cdot t^4-\frac{72802386399015}{37418}\cdot t^2+\frac{4752962138925}{299344}$

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.