Rule: Q[4, 5, 8]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{17}-\frac{7832664}{11003}\cdot t^{15}+\frac{652667928}{55015}\cdot t^{13}-\frac{5229229734}{55015}\cdot t^{11}+\frac{107801282178}{275075}\cdot t^9-\frac{454972876533}{550150}\cdot t^7+\frac{461002317867}{550150}\cdot t^5-\frac{157900293621}{440120}\cdot t^3+\frac{44369803107}{880240}\cdot t$

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.