Rule: Q[2, 14, 25]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{16}-\frac{935281}{4314}\cdot t^{14}+\frac{38001691}{8628}\cdot t^{12}-\frac{245286041}{5752}\cdot t^{10}+\frac{2383796415}{11504}\cdot t^8-\frac{11245499265}{23008}\cdot t^6+\frac{22854346515}{46016}\cdot t^4-\frac{15081381315}{92032}\cdot t^2+\frac{1321665345}{184064}$
• $P_3$:
  $4\cdot t^{41}-\frac{36536974694389094843212509710635785995330102214740239325090121926765779672113742201}{32150743854912056419033642393750760042974640151649777114354423296475175400730794}\cdot t^{39}+\frac{9259868215363355243689200919527550291020978495319500146757339170835263350661422092211}{64301487709824112838067284787501520085949280303299554228708846592950350801461588}\cdot t^{37}-\frac{462447457979799083176873521359164470440448877604339894829759851482460578030562407789761}{42867658473216075225378189858334346723966186868866369485805897728633567200974392}\cdot t^{35}+\frac{45776370905664007030888923307200637701903101647584989044325966540055022169509708078786815}{85735316946432150450756379716668693447932373737732738971611795457267134401948784}\cdot t^{33}-\frac{1585060310564307642449504145356768830143045303709391703025508134739337644151986286839537745}{85735316946432150450756379716668693447932373737732738971611795457267134401948784}\cdot t^{31}+\frac{79344071084585707551349204790445447298870654935203233221698944389279793299512748223447250595}{171470633892864300901512759433337386895864747475465477943223590914534268803897568}\cdot t^{29}-\frac{2925793443979718949426878216714613608478811977771785032966552336865135452340379067292746590495}{342941267785728601803025518866674773791729494950930955886447181829068537607795136}\cdot t^{27}+\frac{80281085711114562781916785777749715513638845987368173667567923015839624344272543221373847982685}{685882535571457203606051037733349547583458989901861911772894363658137075215590272}\cdot t^{25}-\frac{411258558565986546787726921990764449704867563072561107404289580827497606081088872343995105282125}{342941267785728601803025518866674773791729494950930955886447181829068537607795136}\cdot t^{23}+\frac{6281500670342710996702938352542903865120309229832848447210152043592644973290568129154887429000375}{685882535571457203606051037733349547583458989901861911772894363658137075215590272}\cdot t^{21}-\frac{64095839865757365706766139166854327996365117697530269326592590843346573431863103540385508025375}{1238055118360031053440525338868861999248120920400472764933022317072449594251968}\cdot t^{19}+\frac{293502141673042590436376580419950077954086477364112898812658344314814430524029047194532893952380875}{1371765071142914407212102075466699095166917979803723823545788727316274150431180544}\cdot t^{17}-\frac{13923079053948846574541063772965381323253813158842071921198789895356176603125019422978502097706015375}{21948241138286630515393633207467185522670687676859581176732619637060386406898888704}\cdot t^{15}+\frac{57622461937705910509286910269435145645319700012068398739825145576742213945310441671822355955342038125}{43896482276573261030787266414934371045341375353719162353465239274120772813797777408}\cdot t^{13}-\frac{159851360409156031359691484202767240696102148670238048347000480298567777184255792734375894116842440625}{87792964553146522061574532829868742090682750707438324706930478548241545627595554816}\cdot t^{11}+\frac{279115522286207473254642472688860495358158390460184385152389053203937935276283302125512878363975493125}{175585929106293044123149065659737484181365501414876649413860957096483091255191109632}\cdot t^9-\frac{549813201564225037357668732207353973154889250840852886075156979588195840435793169846466307860055733125}{702343716425172176492596262638949936725462005659506597655443828385932365020764438528}\cdot t^7+\frac{242433021364848837771831353767583860301010189797732276229929339664139216885174211745279768171974724375}{1404687432850344352985192525277899873450924011319013195310887656771864730041528877056}\cdot t^5-\frac{23068971148632182727388035650359331397703705095394716608431201336821784563630846612371768430774909375}{2809374865700688705970385050555799746901848022638026390621775313543729460083057754112}\cdot t^3+\frac{347056281150675885231842479960558287667080986292315542772540052936826878495315072540110649501040625}{5618749731401377411940770101111599493803696045276052781243550627087458920166115508224}\cdot t$

Warning: This rule has negative weights!

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.