Rule: Q[4, 5, 10]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^9-21\cdot t^7+108\cdot t^5-135\cdot t^3+45\cdot t$
• $P_3$:
  $t^{19}-\frac{8377498086}{68215861}\cdot t^{17}+\frac{57601919589}{9745123}\cdot t^{15}-\frac{9837542257155}{68215861}\cdot t^{13}+\frac{131441284093635}{68215861}\cdot t^{11}-\frac{970062879190185}{68215861}\cdot t^9+\frac{543834376395255}{9745123}\cdot t^7-\frac{1045646903415015}{9745123}\cdot t^5+\frac{867789327309300}{9745123}\cdot t^3-\frac{239747148335475}{9745123}\cdot t$

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.