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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{19}-\frac{67019984688}{68215861}\cdot t^{17}+\frac{230407678356}{9745123}\cdot t^{15}-\frac{19675084514310}{68215861}\cdot t^{13}+\frac{131441284093635}{68215861}\cdot t^{11}-\frac{970062879190185}{136431722}\cdot t^9+\frac{543834376395255}{38980492}\cdot t^7-\frac{1045646903415015}{77960984}\cdot t^5+\frac{216947331827325}{38980492}\cdot t^3-\frac{239747148335475}{311843936}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.