Rule: Q[12, 19]

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.

• $P_1$:
  $t^{12}-66\cdot t^{10}+1485\cdot t^8-13860\cdot t^6+51975\cdot t^4-62370\cdot t^2+10395$
• $P_2$:
  $t^{31}-\frac{2116422576}{6191363}\cdot t^{29}+\frac{312315913191}{6191363}\cdot t^{27}-\frac{26259673964598}{6191363}\cdot t^{25}+\frac{1398913205740875}{6191363}\cdot t^{23}-\frac{49690386691151220}{6191363}\cdot t^{21}+\frac{1206619116618088215}{6191363}\cdot t^{19}-\frac{20214059593797457290}{6191363}\cdot t^{17}+\frac{232994755858705193745}{6191363}\cdot t^{15}-\frac{1822790280084794080200}{6191363}\cdot t^{13}+\frac{9432838402471077518925}{6191363}\cdot t^{11}-\frac{30971150712054099196650}{6191363}\cdot t^9+\frac{60404032344599956037025}{6191363}\cdot t^7-\frac{62796054487194584255700}{6191363}\cdot t^5+\frac{28569575948565113587125}{6191363}\cdot t^3-\frac{3613936658267491305750}{6191363}\cdot t$

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.