Rule: Q[4, 49]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{53}-\frac{963737155258054627230282435596990792492848}{93327259163492604202079550460405149381}\cdot t^{51}+\frac{4306875066935826918967043397925428137971331092}{1399908887452389063031193256906077240715}\cdot t^{49}-\frac{262389134353322362241935664250115219949218694032}{466636295817463021010397752302025746905}\cdot t^{47}+\frac{1433895292408893970637290030137358993710092919626}{20288534600759261783060771839218510735}\cdot t^{45}-\frac{8779317343114407164644387492789542216789748280686}{1352568973383950785537384789281234049}\cdot t^{43}+\frac{1222205070591677918422504227073544002380274164130377}{2705137946767901571074769578562468098}\cdot t^{41}-\frac{33006219026895689542891620372589491266579960049830157}{1352568973383950785537384789281234049}\cdot t^{39}+\frac{22477533112029903206427642275988625403708835410237449491}{21641103574143212568598156628499744784}\cdot t^{37}-\frac{761552406566188590367505149755086025389683184389536931929}{21641103574143212568598156628499744784}\cdot t^{35}+\frac{82655323607513830610994298773911001871169798890895230693845}{86564414296572850274392626513998979136}\cdot t^{33}-\frac{225181019912039486669053400401035636605767506470689492475265}{10820551787071606284299078314249872392}\cdot t^{31}+\frac{31545500243956613246758681858573408626338140064266793311375665}{86564414296572850274392626513998979136}\cdot t^{29}-\frac{442884349684913704898119104136828919820582822472599829674664545}{86564414296572850274392626513998979136}\cdot t^{27}+\frac{19851174439744035105484867490465732112115498420945050001185066195}{346257657186291401097570506055995916544}\cdot t^{25}-\frac{88155949895383430830676525650385981760222214620317659655081888625}{173128828593145700548785253027997958272}\cdot t^{23}+\frac{19667629618245547729502461417084662909692641806501983691280709820375}{5540122514980662417561128096895934664704}\cdot t^{21}-\frac{106261596929045086919325715240898168703765520743760896644063464517625}{5540122514980662417561128096895934664704}\cdot t^{19}+\frac{1750124560558320119063288391842716850775534581480939435399423876339625}{22160490059922649670244512387583738658816}\cdot t^{17}-\frac{1343462434348921293039921075928007180023173392568161043230428245652125}{5540122514980662417561128096895934664704}\cdot t^{15}+\frac{23921765343547934990831051931646690822356975860154357651090637805731875}{44320980119845299340489024775167477317632}\cdot t^{13}-\frac{37163438076816686163791872521628023123873488295295225153670638297344375}{44320980119845299340489024775167477317632}\cdot t^{11}+\frac{153034711280026041283654822391652502625533951304491246168896743488370625}{177283920479381197361956099100669909270528}\cdot t^9-\frac{48436920343532269238904393037870529659902492147112776283172387855060625}{88641960239690598680978049550334954635264}\cdot t^7+\frac{268606742965148712233673923894868265805527640153244406185088255580683125}{1418271363835049578895648792805359274164224}\cdot t^5-\frac{41565387385311440892199414975030888523975151266968187744689749050784375}{1418271363835049578895648792805359274164224}\cdot t^3+\frac{7233185736413139754813855578736257141339775088057493766028685415621875}{5673085455340198315582595171221437096656896}\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.