Rule: Q[8, 15]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{23}-\frac{28993664}{1105}\cdot t^{21}+\frac{1218982464}{1105}\cdot t^{19}-\frac{27469138592}{1105}\cdot t^{17}+\frac{72832176032}{221}\cdot t^{15}-\frac{587557652304}{221}\cdot t^{13}+\frac{222176447976}{17}\cdot t^{11}-\frac{649351429188}{17}\cdot t^9+\frac{1069116542109}{17}\cdot t^7-\frac{1796386301325}{34}\cdot t^5+\frac{1274070981645}{68}\cdot t^3-\frac{242579663865}{136}\cdot t$

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.