Rule: Q[10, 20]

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.

• $P_1$:
  $t^{10}-45\cdot t^8+630\cdot t^6-3150\cdot t^4+4725\cdot t^2-945$
• $P_2$:
  $t^{30}-\frac{30861963315}{90446489}\cdot t^{28}+\frac{58594047285555}{1175804357}\cdot t^{26}-\frac{4824067950762525}{1175804357}\cdot t^{24}+\frac{30017137132193625}{142130197}\cdot t^{22}-\frac{13174180849381278015}{1847692561}\cdot t^{20}+\frac{297852724847499221475}{1847692561}\cdot t^{18}-\frac{4527397508382980403525}{1847692561}\cdot t^{16}+\frac{45825643716885858121875}{1847692561}\cdot t^{14}-\frac{23217541605513135001125}{142130197}\cdot t^{12}+\frac{8693651240836419512475}{12920927}\cdot t^{10}-\frac{20999445685393754305125}{12920927}\cdot t^8+\frac{26771564505690036293625}{12920927}\cdot t^6-\frac{15034567253335707616875}{12920927}\cdot t^4+\frac{2726884722974218419375}{12920927}\cdot t^2-\frac{99673906355990591625}{12920927}$

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.