Rule: Q[2, 7, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^9-\frac{173}{5}\cdot t^7+\frac{1743}{5}\cdot t^5-1113\cdot t^3+798\cdot t$
• $P_3$:
  $t^{25}-\frac{1998271118619436701}{8668431607928285}\cdot t^{23}+\frac{1110940457535288120331}{50276903325984053}\cdot t^{21}-\frac{3193129745837663521251159}{2765229682929122915}\cdot t^{19}+\frac{501641788199872874368428992}{13826148414645614575}\cdot t^{17}-\frac{9866485266684488257413190502}{13826148414645614575}\cdot t^{15}+\frac{24556924537063223375525157066}{2765229682929122915}\cdot t^{13}-\frac{191331382580401935250738474206}{2765229682929122915}\cdot t^{11}+\frac{16445562475294184528223386277}{50276903325984053}\cdot t^9-\frac{222571687427214277786313843709}{251384516629920265}\cdot t^7+\frac{312026495095950148930485331899}{251384516629920265}\cdot t^5-\frac{1300279447112577931849497921}{1733686321585657}\cdot t^3+\frac{6437953764527756999871721014}{50276903325984053}\cdot t$

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.