Rule: Q[2, 9, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{11}-\frac{1238}{7}\cdot t^9+\frac{15354}{7}\cdot t^7-9783\cdot t^5+\frac{59445}{4}\cdot t^3-\frac{41985}{8}\cdot t$
• $P_3$:
  $4\cdot t^{27}-\frac{2809633265475953984288974}{4958190867002746465323}\cdot t^{25}+\frac{7593751857289589448719033902}{223118589015123590939535}\cdot t^{23}-\frac{254178595137296829547434316667}{223118589015123590939535}\cdot t^{21}+\frac{90824376169734906791948145379}{3863525350911231011940}\cdot t^{19}-\frac{26572855394364317336340731236277}{84997557720047082262680}\cdot t^{17}+\frac{23146683910337962358359130563237}{8499755772004708226268}\cdot t^{15}-\frac{87820744782761592504905540359003}{5666503848003138817512}\cdot t^{13}+\frac{233077560600955963550875088021761}{4121093707638646412736}\cdot t^{11}-\frac{1051284682597935170653095980698741}{8242187415277292825472}\cdot t^9+\frac{152961891001728755900977119263791}{915798601697476980608}\cdot t^7-\frac{209194459342227207076843230407155}{1831597203394953961216}\cdot t^5+\frac{244738883346212509191217387702595}{7326388813579815844864}\cdot t^3-\frac{38108033685825223512125112772575}{14652777627159631689728}\cdot t$

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.