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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{12}-\frac{8477}{76}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{152}\cdot t^6+\frac{1500975}{304}\cdot t^4-\frac{2132865}{1216}\cdot t^2+\frac{110565}{2432}$
• $P_3$:
  $4\cdot t^{32}-\frac{5847620745189902742312521012110897533368147}{7600471364861353424505389778075954003636}\cdot t^{30}+\frac{12644919256579524947979482260018581816939281405}{197612255486395189037140134229974804094536}\cdot t^{28}-\frac{400081122936175138642196911504582436092164621435}{131741503657596792691426756153316536063024}\cdot t^{26}+\frac{20387375050055854407467598019974488298066909893475}{222947160035933033785491433490227984106656}\cdot t^{24}-\frac{1522385358845467078408382927315819048923215938295165}{828089451562036982631825324392275369539008}\cdot t^{22}+\frac{41904237470502697430180905903826422602052206311645415}{1656178903124073965263650648784550739078016}\cdot t^{20}-\frac{41952635304563581114980113016941223658050145132098825}{174334621381481470027752699872057972534528}\cdot t^{18}+\frac{550422197946624621101871726504213339736118711393236575}{348669242762962940055505399744115945069056}\cdot t^{16}-\frac{378563398035402929896354780909622864881328233518424125}{53641421963532760008539292268325530010624}\cdot t^{14}+\frac{2254606905797397966628367821028430378115332231652685775}{107282843927065520017078584536651060021248}\cdot t^{12}-\frac{784303541308147068037591257220146515412651314346815025}{19505971623102821821287015370300192731136}\cdot t^{10}+\frac{1826077878127422869117590804766795199448837279438683375}{39011943246205643642574030740600385462272}\cdot t^8-\frac{2382857907098257288043739709148052026093821589381860875}{78023886492411287285148061481200770924544}\cdot t^6+\frac{1531068050906325208945142813676560370504414260426870625}{156047772984822574570296122962401541849088}\cdot t^4-\frac{381088649079207763590906173170080165396167218090342125}{312095545969645149140592245924803083698176}\cdot t^2+\frac{16984151079881543696955123867821982132533224854625875}{624191091939290298281184491849606167396352}$

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.