Rule: Q[4, 10, 21]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{14}-\frac{477}{7}\cdot t^{12}+\frac{11241}{7}\cdot t^{10}-\frac{112815}{7}\cdot t^8+68715\cdot t^6-108945\cdot t^4+46845\cdot t^2-2835$
• $P_3$:
  $t^{35}-\frac{14602558521974242835294663578251}{34192744932325195010790009931}\cdot t^{33}+\frac{35430736227998594174048418889694574}{444505684120227535140270129103}\cdot t^{31}-\frac{26739889816070122155506965583817256710}{3111539788841592745981890903721}\cdot t^{29}+\frac{1855295758756521871633264433905809458370}{3111539788841592745981890903721}\cdot t^{27}-\frac{961248181396554029139704600388855863542290}{34226937677257520205800799940931}\cdot t^{25}+\frac{31611817456056376264629221144820881717585790}{34226937677257520205800799940931}\cdot t^{23}-\frac{105098839146474992485655693827634676320111910}{4889562525322502886542971420133}\cdot t^{21}+\frac{1736779187201763322549255875828903007240479300}{4889562525322502886542971420133}\cdot t^{19}-\frac{20281838454596826863278878948407539499290242600}{4889562525322502886542971420133}\cdot t^{17}+\frac{165285300057057092984969360561723286175328907150}{4889562525322502886542971420133}\cdot t^{15}-\frac{920442044629788177877472185881060033366563608650}{4889562525322502886542971420133}\cdot t^{13}+\frac{261088255264203182077630300596751590178653951150}{376120194255577145118690109241}\cdot t^{11}-\frac{55351148663453854916098251443928134075256834750}{34192744932325195010790009931}\cdot t^9+\frac{10875289396171623593266363308793580272520589750}{4884677847475027858684287133}\cdot t^7-\frac{7832002179841938121196963320382740906788095250}{4884677847475027858684287133}\cdot t^5+\frac{2299898045864887188776939493575407290648603375}{4884677847475027858684287133}\cdot t^3-\frac{128915419102045609903091065023757731672658875}{4884677847475027858684287133}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.