Rule: Q[3, 6, 24]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^9-\frac{117}{4}\cdot t^7+\frac{945}{4}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{4}\cdot t$
• $P_3$:
  $t^{33}-\frac{243940980213971515758845067}{583136734238195996993980}\cdot t^{31}+\frac{844469415554230186722150320049}{11079597950525723942885620}\cdot t^{29}-\frac{17705815728557592063144436202015}{2215919590105144788577124}\cdot t^{27}+\frac{1189008071840040006487669224341067}{2215919590105144788577124}\cdot t^{25}-\frac{53908760043517619773098799116865065}{2215919590105144788577124}\cdot t^{23}+\frac{1695359351418048547472692485385337745}{2215919590105144788577124}\cdot t^{21}-\frac{1969695233123462608562267653961195265}{116627346847639199398796}\cdot t^{19}+\frac{30549610765405777317742318843333941525}{116627346847639199398796}\cdot t^{17}-\frac{330047594045449206952618024237711122525}{116627346847639199398796}\cdot t^{15}+\frac{2437149593165955203817741483210756509325}{116627346847639199398796}\cdot t^{13}-\frac{150824720942474203427448644807005422225}{1476295529716951891124}\cdot t^{11}+\frac{36705782824710953131545638183054577510075}{116627346847639199398796}\cdot t^9-\frac{66134234760488153521460100553663502114625}{116627346847639199398796}\cdot t^7+\frac{62533314255554403852176814422191394021625}{116627346847639199398796}\cdot t^5-\frac{338726470968762138828695951585549911125}{1476295529716951891124}\cdot t^3+\frac{3983890012170935838727227099340744906875}{116627346847639199398796}\cdot t$

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.