Rule: Q[2, 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.

$P_{1}$ :
$t^{2} - 1$
$P_{2}$ :
$t^{9} - \frac{173}{5} \cdot t^{7} + \frac{1743}{5} \cdot t^{5} - 1113 \cdot t^{3} + 798 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-2.585563514939064629e-187 - 4.0219876899052116452e-187j	4.3e-186, 4.3e-186j
1 - 3.4247021078256297496e-195j	5.77e-63, 5.77e-63j
-4.4288667337963182986 + 4.0825630519695636625e-202j	8.17e-62, 8.17e-62j
2.0314545988278380851 + 1.9137014306107329668e-203j	4.13e-62, 4.13e-62j
4.4288667337963182986 - 1.7131116322198944202e-206j	8.17e-62, 8.17e-62j
3.1397980296785904718 - 2.9008355198595578362e-216j	1.01e-61, 1.01e-61j
-2.0314545988278380851 + 1.0806454419566533849e-224j	4.13e-62, 4.13e-62j
-1 + 3.2205743847985666541e-232j	5.77e-63, 5.77e-63j
-3.1397980296785904718 + 2.3432762717119233669e-243j	1.34e-61, 1.34e-61j

Weights

Weight (ball center)	Error (ball radius)
0.3969924812030075188 - 1.0814848771986537568e-195j	1.67e-25, 2.17e-56j
0.24437548487199379364 + 1.2356145313338163614e-187j	1.12e-25, 1.46e-56j
3.2127309356722662416e-05 + 2.6071506921442275537e-190j	2.45e-28, 3.19e-59j
0.05371667643564092612 - 2.7378297352383466592e-188j	5.05e-26, 6.57e-57j
3.2127309356722662416e-05 - 2.6071506837413814717e-190j	6.51e-29, 8.47e-60j
0.0033794707815047981805 + 4.1550226428369970181e-189j	1.14e-27, 1.49e-58j
0.05371667643564092612 + 2.7378297593340608612e-188j	7.87e-28, 1.03e-58j
0.24437548487199379364 - 1.2356145227374383144e-187j	2.3e-27, 3.01e-58j
0.0033794707815047981805 - 4.1550226627873511527e-189j	1.14e-28, 1.47e-59j

Download

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