Rule: Q[1, 2, 8, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^{11}-\frac{149}{3}\cdot t^9+399\cdot t^7-\frac{2457}{2}\cdot t^5+\frac{10605}{8}\cdot t^3-\frac{5355}{16}\cdot t$
• $P_4$:
  $2\cdot t^{31}-\frac{839960958043992074604091}{2365356289365091915347}\cdot t^{29}+\frac{2698037903741261798437846981}{99344964153333860444574}\cdot t^{27}-\frac{338615629034213939422960946901}{286996563109631152395436}\cdot t^{25}+\frac{18567379275860563346158780812975}{573993126219262304790872}\cdot t^{23}-\frac{96492572023781136168310663908825}{163998036062646372797392}\cdot t^{21}+\frac{183450007534697194219496911709775}{25230467086560980430368}\cdot t^{19}-\frac{40363279205729767325022504147850575}{655992144250585491189568}\cdot t^{17}+\frac{465959432528072010082336333496199975}{1311984288501170982379136}\cdot t^{15}-\frac{278069518359491907958617208562638875}{201843736692487843442944}\cdot t^{13}+\frac{1411180472218607278042279672274126625}{403687473384975686885888}\cdot t^{11}-\frac{4488675124281877372533298302559870125}{807374946769951373771776}\cdot t^9+\frac{1196634927084926705618126933082461625}{230678556219986106791936}\cdot t^7-\frac{1180710553849397652456998867946623625}{461357112439972213583872}\cdot t^5+\frac{516885121451999669467183496495431875}{922714224879944427167744}\cdot t^3-\frac{68540125432790089255610669508669375}{1845428449759888854335488}\cdot t$

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.