Rule: Q[1, 8, 18]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-36\cdot t^7+378\cdot t^5-1260\cdot t^3+945\cdot t$
• $P_3$:
  $t^{27}-\frac{714658329}{2285023}\cdot t^{25}+\frac{94140973278}{2285023}\cdot t^{23}-\frac{75557276706006}{25135253}\cdot t^{21}+\frac{16896449197580211}{125676265}\cdot t^{19}-\frac{484421864565957381}{125676265}\cdot t^{17}+\frac{9051999606133351308}{125676265}\cdot t^{15}-\frac{1692532392766158132}{1933481}\cdot t^{13}+\frac{1194206228993423709}{175771}\cdot t^{11}-\frac{5707020368910312459}{175771}\cdot t^9+\frac{15785851898960492454}{175771}\cdot t^7-\frac{22744883366833267962}{175771}\cdot t^5+\frac{14009296299489055215}{175771}\cdot t^3-\frac{2310749345160580905}{175771}\cdot t$

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.