Rule: Q[4, 5]

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.

$P_{1}$ :
$t^{4} - 6 \cdot t^{2} + 3$
$P_{2}$ :
$t^{9} - 21 \cdot t^{7} + 108 \cdot t^{5} - 135 \cdot t^{3} + 45 \cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
3.7313022243357029508 - 1.8033161362862765197e-130j	1.71e-62, 1.71e-62j
-2.3344142183389772393 + 0j	2.55e-62, 2.55e-62j
2.3344142183389772393 - 5.635362925894614124e-132j	2.55e-62, 2.55e-62j
-3.7313022243357029508 + 3.3019704643913754633e-134j	1.31e-62, 1.31e-62j
-1.0379709584894152952 + 0j	1.32e-62, 1.32e-62j
1.0379709584894152952 - 1.3120851772591970218e-140j	1.32e-62, 1.32e-62j
0.74196378430272585765 - 1.1456011363123517558e-151j	6.72e-63, 6.72e-63j
4.1402108026390475844e-171 + 1.6560843210556190338e-170j	1.54e-169, 1.54e-169j
-0.74196378430272585765 + 3.6772458879133363613e-186j	8.43e-63, 8.43e-63j

Weights

Weight (ball center)	Error (ball radius)
0.00059220888055192656046 + 2.6527786096182351943e-133j	4.74e-30, 4.65e-61j
0.033742373970539285842 - 3.2028324863850529288e-133j	6.98e-29, 6.85e-60j
0.033742373970539285842 - 1.1647609448259264248e-132j	6.53e-29, 6.41e-60j
0.00059220888055192656046 + 1.2827860451314736594e-134j	1.46e-30, 1.43e-61j
0.37641928537232163666 + 1.2488224203801158376e-131j	1.87e-27, 1.82e-58j
0.37641928537232163666 + 2.065550627341561193e-131j	9.35e-28, 9.09e-59j
-0.17742053489007951573 - 3.1887415690461141267e-131j	1.4e-27, 1.36e-58j
0.53333333333333333333 + 2.2199990592226427864e-131j	4.9e-28, 4.71e-59j
-0.17742053489007951573 - 2.2249366906930763442e-131j	3.51e-28, 3.43e-59j

Download

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