Rule: Q[2, 12]

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.

$P_{1}$ :
$t^{2} - 1$
$P_{2}$ :
$t^{14} - \frac{124249}{1555} \cdot t^{12} + \frac{3530769}{1555} \cdot t^{10} - \frac{8883963}{311} \cdot t^{8} + \frac{50229333}{311} \cdot t^{6} - \frac{114812775}{311} \cdot t^{4} + \frac{78937551}{311} \cdot t^{2} - \frac{6151761}{311}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
3.6069468897368460303 - 9.3229259140002584291e-156j	1.59e-60, 1.59e-60j
4.6254356317132469284 - 1.5262473102848585015e-166j	1.87e-60, 1.87e-60j
-2.6788642116343808239 + 2.2641777826932291477e-171j	7.23e-61, 7.23e-61j
-5.8272369191325365786 + 3.7803682621753022377e-172j	7.87e-61, 7.87e-61j
-3.6069468897368460303 + 1.0027073037641443368e-171j	1.63e-60, 1.63e-60j
1.8100151044187559318 - 1.1624127009362560357e-173j	2.36e-61, 2.36e-61j
-4.6254356317132469284 - 4.0101066555311991719e-177j	1.75e-60, 1.75e-60j
-1 + 1.3881138422992612518e-178j	2.71e-62, 2.71e-62j
0.2983537964726121739 + 5.0126333194139989649e-179j	4.31e-63, 4.31e-63j
5.8272369191325365786 - 2.2969548714261864247e-181j	6.93e-61, 6.93e-61j
1 - 1.7007262231599180671e-185j	2.85e-62, 2.85e-62j
2.6788642116343808239 + 1.4027579833653779454e-189j	7.15e-61, 7.15e-61j
-0.2983537964726121739 + 9.6988633913030530018e-197j	3.1e-63, 3.1e-63j
-1.8100151044187559318 + 3.5273344769017030044e-199j	1.93e-61, 1.93e-61j

Weights

Weight (ball center)	Error (ball radius)
0.0005760291082305695096 + 1.1119155436968229586e-158j	9.11e-23, 1.35e-52j
9.7819999278132357203e-06 + 5.3973185202777729158e-160j	3.22e-24, 4.76e-54j
0.0098809886556137197268 + 4.6945378949957964421e-159j	1.53e-22, 2.26e-52j
2.3154831845211237908e-08 - 2.2597540564883788775e-162j	5.37e-27, 7.96e-57j
0.0005760291082305695096 - 7.4443523352241778371e-160j	1.39e-24, 2.06e-54j
0.065313216080933070583 + 6.0205936955578014952e-158j	7.88e-23, 1.17e-52j
9.7819999278132357203e-06 + 6.6774207046244891459e-161j	6.73e-26, 9.96e-56j
0.1862254014094946888 + 6.294336409661304527e-158j	2.42e-22, 3.76e-52j
0.23799455959096829293 + 1.5829421452947561391e-157j	1.36e-22, 2.1e-52j
2.3154831845211237908e-08 - 9.601869507785609943e-162j	8.31e-28, 1.23e-57j
0.1862254014094946888 - 1.1123231416648262064e-157j	3.61e-23, 5.65e-53j
0.0098809886556137197268 - 3.1795635359272470926e-158j	2.1e-24, 3.11e-54j
0.23799455959096829293 - 1.3410776454301926093e-157j	3.12e-23, 5.28e-53j
0.065313216080933070583 - 1.9971704046843678072e-158j	6.31e-24, 8.51e-54j

Download

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