Rule: Q[4]

Type

This rule is of Hermite (physicists') type.

Polynomials

One starts from the polynomial $P_{1}$ and extends one by one with $P_{i}$ 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.

$P_{1}$ :
$16 \cdot t^{4} - 48 \cdot t^{2} + 12$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
1.6506801238857845559 - 1.7362464340324407525e-63j	8.65e-63, 8.65e-63j
-0.52464762327529031788 - 6.788658728877023275e-77j	1.01e-63, 1.01e-63j
-1.6506801238857845559 - 2.6028904508071622781e-96j	1.11e-63, 1.11e-63j
0.52464762327529031788 - 1.0151767349262596893e-115j	1.01e-63, 1.01e-63j

Weights

Weight (ball center)	Error (ball radius)
0.045875854768068491817 + 1.3147962534567034171e-64j	1.68e-31, 4.7e-63j
0.45412414523193150818 + 1.1520359947785274145e-64j	9.03e-31, 1.66e-62j
0.045875854768068491817 - 2.4126960789281647132e-65j	1.02e-31, 2.85e-63j
0.45412414523193150818 - 2.2255626403424143602e-64j	6.23e-31, 1.04e-62j

Download

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