Rule: Q[2, 3, 30]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{35}-\frac{68846340047732409363835016641}{63227392892962910859160634}\cdot t^{33}+\frac{2367564651603713669857353746679}{18064969397989403102617324}\cdot t^{31}-\frac{2333691488154707773585955043094185}{252909571571851643436642536}\cdot t^{29}+\frac{30621734494585059989834459689485885}{72259877591957612410469296}\cdot t^{27}-\frac{1937332891052733362494069706446855845}{144519755183915224820938592}\cdot t^{25}+\frac{86926297719563174817810777355020553275}{289039510367830449641877184}\cdot t^{23}-\frac{2806899376703369914691589984408081582075}{578079020735660899283754368}\cdot t^{21}+\frac{65531580050397733340081217924981898976625}{1156158041471321798567508736}\cdot t^{19}-\frac{1102432044747529245586899432849315422961375}{2312316082942643597135017472}\cdot t^{17}+\frac{13218345042809828466067591589046118541359125}{4624632165885287194270034944}\cdot t^{15}-\frac{110814785337642907245463434996697177417762125}{9249264331770574388540069888}\cdot t^{13}+\frac{630725838101622388856010323993360236236786375}{18498528663541148777080139776}\cdot t^{11}-\frac{2332962190056478136995217363274353516992914375}{36997057327082297554160279552}\cdot t^9+\frac{5248097383577596322998342098484204439440325625}{73994114654164595108320559104}\cdot t^7-\frac{6452457046425266291928538840323358106347715625}{147988229308329190216641118208}\cdot t^5+\frac{3571266257783259757734601384452555209105169375}{295976458616658380433282236416}\cdot t^3-\frac{283017090170541331628942043875739534919749375}{295976458616658380433282236416}\cdot t$

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.