Rule: Q[12, 21]

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.

• $P_1$:
  $t^{12}-66\cdot t^{10}+1485\cdot t^8-13860\cdot t^6+51975\cdot t^4-62370\cdot t^2+10395$
• $P_2$:
  $t^{33}-\frac{1324463019}{3091984}\cdot t^{31}+\frac{200577548160}{2512237}\cdot t^{29}-\frac{343933605133635}{40195792}\cdot t^{27}+\frac{11800013774900175}{20097896}\cdot t^{25}-\frac{1093070447790596055}{40195792}\cdot t^{23}+\frac{1254116412737264835}{1435564}\cdot t^{21}-\frac{113144489909606783925}{5742256}\cdot t^{19}+\frac{47216958813223825725}{151112}\cdot t^{17}-\frac{1044815980504160192625}{302224}\cdot t^{15}+\frac{991113838582300856775}{37778}\cdot t^{13}-\frac{3086482588843958417025}{23248}\cdot t^{11}+\frac{4986513451688993222625}{11624}\cdot t^9-\frac{19245077839616143717125}{23248}\cdot t^7+\frac{4975584239837721943125}{5812}\cdot t^5-\frac{9059923977142930439625}{23248}\cdot t^3+\frac{573488939085422196375}{11624}\cdot t$

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.