Rule: Q[3, 20]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{23}-\frac{435401548}{466119}\cdot t^{21}+\frac{6984086690}{155373}\cdot t^{19}-\frac{60312139755}{51791}\cdot t^{17}+\frac{922682751235}{51791}\cdot t^{15}-\frac{17221241659335}{103582}\cdot t^{13}+\frac{195859892055555}{207164}\cdot t^{11}-\frac{1318771477098075}{414328}\cdot t^9+\frac{9887794220979675}{1657312}\cdot t^7-\frac{18448838678845575}{3314624}\cdot t^5+\frac{13826157508738575}{6629248}\cdot t^3-\frac{2510039001444975}{13258496}\cdot t$

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.