Rule: Q[4, 7]

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.

$P_{1}$ :
$t^{4} - 6 \cdot t^{2} + 3$
$P_{2}$ :
$t^{11} - 41 \cdot t^{9} + 528 \cdot t^{7} - 2520 \cdot t^{5} + 4095 \cdot t^{3} - 1575 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.3344142183389772393 - 8.0798859841845769657e-189j	1.1e-61, 1.1e-61j
-3.3747086797406716539 + 0j	1.42e-61, 1.42e-61j
0.74196378430272585765 - 1.6722178260867332762e-198j	5.5e-63, 5.5e-63j
-1.4655215253859805014 + 0j	3.37e-62, 3.37e-62j
3.3747086797406716539 + 0j	1.42e-61, 1.42e-61j
-4.6328811754148542753 + 1.1331388749451397798e-217j	6.13e-62, 6.13e-62j
-2.3344142183389772393 - 8.104840814674900387e-225j	1.08e-61, 1.08e-61j
9.6617231543956999623e-232 - 2.0128589904991041588e-233j	1.06e-230, 1.06e-230j
1.4655215253859805014 + 2.9993936277912619096e-241j	3.37e-62, 3.37e-62j
4.6328811754148542753 + 8.5813340028512818612e-247j	6.13e-62, 6.13e-62j
-0.74196378430272585765 - 2.7934029957198183142e-249j	6.8e-63, 6.8e-63j

Weights

Weight (ball center)	Error (ball radius)
0.025048819878317716795 + 3.9101646372126739528e-190j	7.16e-26, 3.62e-56j
0.0015140568125348532207 - 4.3545698097554131667e-192j	7.77e-28, 3.91e-58j
0.21508206464775363638 + 1.09129836809133892e-189j	7.81e-25, 3.93e-55j
0.10596155113257208488 - 2.2086274062489756304e-190j	6.58e-25, 3.35e-55j
0.0015140568125348532207 + 2.3897824250223408554e-191j	2.97e-28, 1.52e-58j
1.2555147869327766025e-05 + 1.7409329847080854246e-193j	1.38e-29, 6.88e-60j
0.025048819878317716795 + 4.3349549349207174916e-191j	5.44e-27, 2.68e-57j
0.3047619047619047619 - 9.2298797999325146794e-190j	6.26e-26, 3.07e-56j
0.10596155113257208488 - 9.6590088610104620035e-190j	1.31e-26, 6.35e-57j
1.2555147869327766025e-05 - 5.2772541828710524524e-193j	4.12e-30, 2.21e-60j
0.21508206464775363638 + 5.6489760323673004245e-190j	2.41e-26, 9.92e-57j

Download

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