Rule: Q[8, 13]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{21}-\frac{98959616}{5011}\cdot t^{19}+\frac{3055042368}{5011}\cdot t^{17}-\frac{49131344640}{5011}\cdot t^{15}+\frac{449515258080}{5011}\cdot t^{13}-\frac{2402485918560}{5011}\cdot t^{11}+\frac{7421582848680}{5011}\cdot t^9-\frac{12654579777840}{5011}\cdot t^7+\frac{10822722285375}{5011}\cdot t^5-\frac{3844571155425}{5011}\cdot t^3+\frac{1463173536825}{20044}\cdot t$

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.