Rule: Q[3]

Type

This rule is of Hermite (probabilists') type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi 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.

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
-1.7320508075688772935 - 3.042210512962265822e-39j 1.44e-38, 1.44e-38j
3.363654055173458713e-52 - 4.649113003389179817e-52j 1.72e-51, 1.72e-51j
1.7320508075688772935 + 9.2160645636326305332e-69j 2.91e-68, 2.91e-68j

Weights

Weight (ball center) Error (ball radius)
0.16666666666666666667 - 4.3910526464765788559e-40j 1.34e-31, 8.99e-39j
0.66666666666666666667 + 5.854736861967578845e-40j 1.53e-31, 8.3e-39j
0.16666666666666666667 - 1.463684215490999989e-40j 9.54e-32, 6.23e-39j

Download

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