Rule: Q[2, 10, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{12}-\frac{8477}{152}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{76}\cdot t^6+\frac{1500975}{76}\cdot t^4-\frac{2132865}{152}\cdot t^2+\frac{110565}{152}$
• $P_3$:
  $t^{32}-\frac{5847620745189902742312521012110897533368147}{15200942729722706849010779556151908007272}\cdot t^{30}+\frac{12644919256579524947979482260018581816939281405}{197612255486395189037140134229974804094536}\cdot t^{28}-\frac{400081122936175138642196911504582436092164621435}{65870751828798396345713378076658268031512}\cdot t^{26}+\frac{20387375050055854407467598019974488298066909893475}{55736790008983258446372858372556996026664}\cdot t^{24}-\frac{1522385358845467078408382927315819048923215938295165}{103511181445254622828978165549034421192376}\cdot t^{22}+\frac{41904237470502697430180905903826422602052206311645415}{103511181445254622828978165549034421192376}\cdot t^{20}-\frac{41952635304563581114980113016941223658050145132098825}{5447956918171295938367271871001811641704}\cdot t^{18}+\frac{550422197946624621101871726504213339736118711393236575}{5447956918171295938367271871001811641704}\cdot t^{16}-\frac{378563398035402929896354780909622864881328233518424125}{419073609090099687566713220846293203208}\cdot t^{14}+\frac{2254606905797397966628367821028430378115332231652685775}{419073609090099687566713220846293203208}\cdot t^{12}-\frac{784303541308147068037591257220146515412651314346815025}{38097600826372698869701201895117563928}\cdot t^{10}+\frac{1826077878127422869117590804766795199448837279438683375}{38097600826372698869701201895117563928}\cdot t^8-\frac{2382857907098257288043739709148052026093821589381860875}{38097600826372698869701201895117563928}\cdot t^6+\frac{1531068050906325208945142813676560370504414260426870625}{38097600826372698869701201895117563928}\cdot t^4-\frac{381088649079207763590906173170080165396167218090342125}{38097600826372698869701201895117563928}\cdot t^2+\frac{16984151079881543696955123867821982132533224854625875}{38097600826372698869701201895117563928}$

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.