Rule: Q[1, 2, 10, 26]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{13}-\frac{629}{8}\cdot t^{11}+\frac{17435}{8}\cdot t^9-\frac{105435}{4}\cdot t^7+\frac{557865}{4}\cdot t^5-\frac{2248785}{8}\cdot t^3+\frac{1133055}{8}\cdot t$
• $P_4$:
  $t^{39}-\frac{62344019653739501860494948964782623868150229}{107107765571014895711482237366976081467608}\cdot t^{37}+\frac{1233581744529904314609470513581742737711841497885}{8140190183397132074072650039890182191538208}\cdot t^{35}-\frac{190450052906489912692065749584619996195644106830795}{8140190183397132074072650039890182191538208}\cdot t^{33}+\frac{41419600209009034562007305677067523168083740727107195}{17297904139718905657404381334766637157018692}\cdot t^{31}-\frac{175066301769333140233457169580343514664197399121933145}{1017523772924641509259081254986272773942276}\cdot t^{29}+\frac{32656934164920136616048366645889400400865811375206961495}{3641664029414506454190396070477186769898672}\cdot t^{27}-\frac{7967956141139620793661276449581133932940071002880897514625}{23063872186291874209872508446355516209358256}\cdot t^{25}+\frac{114538386211271892544993287568588998740273341104219398430375}{11531936093145937104936254223177758104679128}\cdot t^{23}-\frac{2464033845779568995421369434389334031520340661118437410515875}{11531936093145937104936254223177758104679128}\cdot t^{21}+\frac{1040382453979074178554596810680070099133177055887319055650125}{303472002451208871182533005873098897491556}\cdot t^{19}-\frac{725689826603055442029691917171482693431296825322208578362375}{17851294261835815951913706227829346911268}\cdot t^{17}+\frac{3131054153930636782252718342535849163501155239635446349149375}{8925647130917907975956853113914673455634}\cdot t^{15}-\frac{19212891260161469094091188875725761643023079648839047881258125}{8925647130917907975956853113914673455634}\cdot t^{13}+\frac{648813938120183219863668890785526731072718353449065117001294375}{71405177047343263807654824911317387645072}\cdot t^{11}-\frac{1796402629495949352845955540848191923720541892375483071865570625}{71405177047343263807654824911317387645072}\cdot t^9+\frac{1519959679967665559326370237295005468949299028008415630493385625}{35702588523671631903827412455658693822536}\cdot t^7-\frac{702987496567067711634926914145594171816637244913003162088965625}{17851294261835815951913706227829346911268}\cdot t^5+\frac{2331205017591749907313626444424796214669956704613057825904496875}{142810354094686527615309649822634775290144}\cdot t^3-\frac{274956935804831972811860612795367023122114018353806821174378125}{142810354094686527615309649822634775290144}\cdot t$

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.