Rule: Q[1, 4, 12]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^5-10\cdot t^3+\frac{15}{2}\cdot t$
• $P_3$:
  $2\cdot t^{17}-\frac{6536}{53}\cdot t^{15}+\frac{617205}{212}\cdot t^{13}-\frac{7144995}{212}\cdot t^{11}+\frac{172854825}{848}\cdot t^9-\frac{269555715}{424}\cdot t^7+\frac{3204996795}{3392}\cdot t^5-\frac{1892565675}{3392}\cdot t^3+\frac{1129052925}{13568}\cdot t$

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.