Rule: Q[2, 3, 12]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^{17}-\frac{1927729267}{18122395}\cdot t^{15}+\frac{76689404679}{18122395}\cdot t^{13}-\frac{1451963624397}{18122395}\cdot t^{11}+\frac{2765036333631}{3624479}\cdot t^9-\frac{12957851045997}{3624479}\cdot t^7+\frac{27641768331177}{3624479}\cdot t^5-\frac{23638263740091}{3624479}\cdot t^3+\frac{6464746886598}{3624479}\cdot t$

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.