Rule: Q[2, 5, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^7-\frac{53}{3}\cdot t^5+\frac{215}{3}\cdot t^3-55\cdot t$
• $P_3$:
  $t^{23}-\frac{95280890755795}{454088400077}\cdot t^{21}+\frac{73610338759101533}{4086795600693}\cdot t^{19}-\frac{50596907879744273137}{61301934010395}\cdot t^{17}+\frac{1355961124027817544622}{61301934010395}\cdot t^{15}-\frac{112431828650153050934}{314368892361}\cdot t^{13}+\frac{1094239341459686688994}{314368892361}\cdot t^{11}-\frac{6224775940481682820390}{314368892361}\cdot t^9+\frac{2167197645791877595589}{34929876929}\cdot t^7-\frac{3377729383397684509579}{34929876929}\cdot t^5+\frac{2188577584705176879445}{34929876929}\cdot t^3-\frac{396238218708225835095}{34929876929}\cdot t$

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.