Rule: Q[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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{22}-\frac{167544224}{25259}\cdot t^{20}+\frac{76903663376}{277849}\cdot t^{18}-\frac{1681300056856}{277849}\cdot t^{16}+\frac{21007071848040}{277849}\cdot t^{14}-\frac{11822388845820}{21373}\cdot t^{12}+\frac{4541750070270}{1943}\cdot t^{10}-\frac{10552207604085}{1943}\cdot t^8+\frac{1686288299535}{268}\cdot t^6-\frac{46953925305525}{15544}\cdot t^4+\frac{12547692947475}{31088}\cdot t^2-\frac{263693655225}{62176}$

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.