Rule: Q[2, 3, 6, 16]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{11}-\frac{6923}{164}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{164}\cdot t^5+\frac{1313235}{164}\cdot t^3-\frac{418635}{82}\cdot t$
• $P_4$:
  $t^{27}-\frac{18602579712383878626727500047181374637}{74704257323725979223251765529020284}\cdot t^{25}+\frac{192929105341891780923534882307275370184011}{7395721475048871943101924787373008116}\cdot t^{23}-\frac{55950380084413613458467937165969594423074041}{36978607375244359715509623936865040580}\cdot t^{21}+\frac{663864826594708668963424528982895827637682549}{12326202458414786571836541312288346860}\cdot t^{19}-\frac{3801287791192870507782550586682542459572035613}{3081550614603696642959135328072086715}\cdot t^{17}+\frac{2078590764950990084632582196395305710554955567}{112056385985588968834877648293530426}\cdot t^{15}-\frac{1839187122969481435753377901357387069479940493}{10021302811719338676289870985600282}\cdot t^{13}+\frac{44010590698246551975681326315142359919699322615}{37352128661862989611625882764510142}\cdot t^{11}-\frac{354948968306563035285879570862895401610640869861}{74704257323725979223251765529020284}\cdot t^9+\frac{847268809082663823603602552646224294888980760013}{74704257323725979223251765529020284}\cdot t^7-\frac{1075909353398307023974063851904183537025616991035}{74704257323725979223251765529020284}\cdot t^5+\frac{585959156894788828875873698514534545937251754645}{74704257323725979223251765529020284}\cdot t^3-\frac{38989004364594468641511334375185435705024746445}{37352128661862989611625882764510142}\cdot t$

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.