Rule: Q[3, 8, 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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{11}-\frac{596}{3}\cdot t^9+1596\cdot t^7-4914\cdot t^5+\frac{10605}{2}\cdot t^3-\frac{5355}{4}\cdot t$
• $P_3$:
  $8\cdot t^{33}-\frac{352128240105506857881621355}{189597439925928117909402}\cdot t^{31}+\frac{70469647556337902667730560547}{379194879851856235818804}\cdot t^{29}-\frac{8039357930764015329357528671065}{758389759703712471637608}\cdot t^{27}+\frac{1359038320071302874875649124548321}{3539152211950658200975504}\cdot t^{25}-\frac{65922238821787426099292192900244675}{7078304423901316401951008}\cdot t^{23}+\frac{18482114929426498463347114783251525}{118963099561366662217664}\cdot t^{21}-\frac{429077620177517363177396668029902775}{237926199122733324435328}\cdot t^{19}+\frac{6936712950789970049921300085433237875}{475852398245466648870656}\cdot t^{17}-\frac{77426987547450717866864174174110413675}{951704796490933297741312}\cdot t^{15}+\frac{586081965505491221704912161226985281875}{1903409592981866595482624}\cdot t^{13}-\frac{2922217798003982663649174612142715813625}{3806819185963733190965248}\cdot t^{11}+\frac{9182700087608075206309809999665351275125}{7613638371927466381930496}\cdot t^9-\frac{17016829873838637297785909480870397804375}{15227276743854932763860992}\cdot t^7+\frac{16805397874703921635412245469979708588375}{30454553487709865527721984}\cdot t^5-\frac{7519902533241770412199803266118369298125}{60909106975419731055443968}\cdot t^3+\frac{1079540107983915478600492013258658245625}{121818213950839462110887936}\cdot t$

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.