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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{16}-\frac{935281}{8628}\cdot t^{14}+\frac{38001691}{8628}\cdot t^{12}-\frac{245286041}{2876}\cdot t^{10}+\frac{2383796415}{2876}\cdot t^8-\frac{11245499265}{2876}\cdot t^6+\frac{22854346515}{2876}\cdot t^4-\frac{15081381315}{2876}\cdot t^2+\frac{1321665345}{2876}$
• $P_3$:
  $t^{41}-\frac{36536974694389094843212509710635785995330102214740239325090121926765779672113742201}{64301487709824112838067284787501520085949280303299554228708846592950350801461588}\cdot t^{39}+\frac{9259868215363355243689200919527550291020978495319500146757339170835263350661422092211}{64301487709824112838067284787501520085949280303299554228708846592950350801461588}\cdot t^{37}-\frac{462447457979799083176873521359164470440448877604339894829759851482460578030562407789761}{21433829236608037612689094929167173361983093434433184742902948864316783600487196}\cdot t^{35}+\frac{45776370905664007030888923307200637701903101647584989044325966540055022169509708078786815}{21433829236608037612689094929167173361983093434433184742902948864316783600487196}\cdot t^{33}-\frac{1585060310564307642449504145356768830143045303709391703025508134739337644151986286839537745}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{31}+\frac{79344071084585707551349204790445447298870654935203233221698944389279793299512748223447250595}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{29}-\frac{2925793443979718949426878216714613608478811977771785032966552336865135452340379067292746590495}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{27}+\frac{80281085711114562781916785777749715513638845987368173667567923015839624344272543221373847982685}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{25}-\frac{822517117131973093575453843981528899409735126145122214808579161654995212162177744687990210564250}{5358457309152009403172273732291793340495773358608296185725737216079195900121799}\cdot t^{23}+\frac{12563001340685421993405876705085807730240618459665696894420304087185289946581136258309774858000750}{5358457309152009403172273732291793340495773358608296185725737216079195900121799}\cdot t^{21}-\frac{512766718926058925654129113334834623970920941580242154612740726746772587454904828323084064203000}{19344611224375485210008208419825968738251889381257386952078473704257024910187}\cdot t^{19}+\frac{1174008566692170361745506321679800311816345909456451595250633377259257722096116188778131575809523500}{5358457309152009403172273732291793340495773358608296185725737216079195900121799}\cdot t^{17}-\frac{13923079053948846574541063772965381323253813158842071921198789895356176603125019422978502097706015375}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{15}+\frac{57622461937705910509286910269435145645319700012068398739825145576742213945310441671822355955342038125}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{13}-\frac{159851360409156031359691484202767240696102148670238048347000480298567777184255792734375894116842440625}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^{11}+\frac{279115522286207473254642472688860495358158390460184385152389053203937935276283302125512878363975493125}{10716914618304018806344547464583586680991546717216592371451474432158391800243598}\cdot t^9-\frac{549813201564225037357668732207353973154889250840852886075156979588195840435793169846466307860055733125}{21433829236608037612689094929167173361983093434433184742902948864316783600487196}\cdot t^7+\frac{242433021364848837771831353767583860301010189797732276229929339664139216885174211745279768171974724375}{21433829236608037612689094929167173361983093434433184742902948864316783600487196}\cdot t^5-\frac{23068971148632182727388035650359331397703705095394716608431201336821784563630846612371768430774909375}{21433829236608037612689094929167173361983093434433184742902948864316783600487196}\cdot t^3+\frac{347056281150675885231842479960558287667080986292315542772540052936826878495315072540110649501040625}{21433829236608037612689094929167173361983093434433184742902948864316783600487196}\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 (probabilists') type can be downloaded here packed into a single file.