Rule: Q[4]

Type

This rule is of Hermite (probabilists') 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.

$P_{1}$ :
$t^{4} - 6 \cdot t^{2} + 3$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.3344142183389772393 + 1.2347491373534061824e-141j	5.82e-127, 5.82e-127j
-2.3344142183389772393 - 1.6124904798656661429e-173j	5.82e-127, 5.82e-127j
-0.74196378430272585765 + 9.8493333116648348876e-210j	2.4e-127, 2.4e-127j
0.74196378430272585765 + 7.4984840694781547741e-242j	2.4e-127, 2.4e-127j

Weights

Weight (ball center)	Error (ball radius)
0.045875854768068491817 - 6.6116647575509126775e-143j	3.15e-31, 6.02e-127j
0.045875854768068491817 + 1.2132630887702497852e-143j	1.99e-31, 3.6e-127j
0.45412414523193150818 - 5.7931985781696107534e-143j	1.78e-30, 2.66e-126j
0.45412414523193150818 + 1.1191600246950273646e-142j	1.27e-30, 1.85e-126j

Download

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