Rule: Q[1, 6, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^7-21\cdot t^5+\frac{105}{2}\cdot t^3-\frac{105}{4}\cdot t$
• $P_3$:
  $2\cdot t^{23}-\frac{21735}{83}\cdot t^{21}+\frac{577181955}{41998}\cdot t^{19}-\frac{159660594807}{419980}\cdot t^{17}+\frac{2565337326951}{419980}\cdot t^{15}-\frac{9930055980663}{167992}\cdot t^{13}+\frac{10550934204993}{30544}\cdot t^{11}-\frac{72692461881585}{61088}\cdot t^9+\frac{6739282250883}{2944}\cdot t^7-\frac{1088702779003749}{488704}\cdot t^5+\frac{889027794718245}{977408}\cdot t^3-\frac{8514428328315}{84992}\cdot t$

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.