Rule: Q[4, 22]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{26}-\frac{102411351735864}{45536981123}\cdot t^{24}+\frac{6046204174401376}{45536981123}\cdot t^{22}-\frac{196688689402839480}{45536981123}\cdot t^{20}+\frac{204731552439352785}{2396683217}\cdot t^{18}-\frac{5128120827284581665}{4793366434}\cdot t^{16}+\frac{20566741687898847210}{2396683217}\cdot t^{14}-\frac{104665211154717152940}{2396683217}\cdot t^{12}+\frac{5254134430833607594275}{38346931472}\cdot t^{10}-\frac{19309118339877159768975}{76693862944}\cdot t^8+\frac{2389600191682204526025}{9586732868}\cdot t^6-\frac{8884805855948243696475}{76693862944}\cdot t^4+\frac{11966600238582800886075}{613550903552}\cdot t^2-\frac{666102408269320897875}{1227101807104}$

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.