Rule: Q[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.

$P_{1}$ :
$t^{12} - 66 \cdot t^{10} + 1485 \cdot t^{8} - 13860 \cdot t^{6} + 51975 \cdot t^{4} - 62370 \cdot t^{2} + 10395$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.2594644510007991239 + 1.4246760768554619758e-192j	1.4e-61, 1.4e-61j
-5.5009017044677476008 - 4.1805445652168331904e-199j	2.2e-61, 2.2e-61j
4.271825847932281723 - 1.1462274193762202666e-204j	4.32e-61, 4.32e-61j
5.5009017044677476008 - 9.2826736635505850758e-214j	1.62e-61, 1.62e-61j
-3.2237098287700974717 - 2.7195332998683354714e-217j	4e-61, 4e-61j
3.2237098287700974717 + 8.104840814674900387e-224j	3.24e-61, 3.24e-61j
-2.2594644510007991239 + 2.9548898803502240994e-226j	1.33e-61, 1.33e-61j
-1.3403751971516167215 + 5.2765890720539716061e-228j	2.2e-62, 2.2e-62j
0.4444030019441389453 + 6.5957363400674645076e-229j	3.28e-63, 3.28e-63j
-4.271825847932281723 - 1.710930141924238535e-232j	4.02e-61, 4.02e-61j
1.3403751971516167215 - 3.749242034739077387e-241j	2.56e-62, 2.56e-62j
-0.4444030019441389453 - 4.4694447931517093027e-249j	3.28e-63, 3.28e-63j

Weights

Weight (ball center)	Error (ball radius)
0.029116687912364151216 - 4.6863381260072971236e-194j	6.48e-21, 1.38e-51j
1.4999271676371678258e-07 - 1.2132212160390975497e-197j	1.01e-25, 2.15e-56j
4.8371849225906277786e-05 + 8.4018995499042285016e-196j	2.12e-24, 4.51e-55j
1.4999271676371678258e-07 - 2.9045883020833197261e-197j	9.66e-26, 2.05e-56j
0.0022033806875331988662 - 2.0811330082511107869e-195j	1.33e-24, 2.83e-55j
0.0022033806875331988662 - 1.1834347591983837068e-194j	8.65e-24, 1.85e-54j
0.029116687912364151216 + 9.1795754357083733419e-195j	6.34e-24, 1.36e-54j
0.146967048045329988 - 2.5888920825182302513e-194j	3.16e-23, 6.85e-54j
0.32166436151282999193 - 7.596215169276488168e-194j	4.15e-23, 8.37e-54j
4.8371849225906277786e-05 + 2.5887164102995393046e-196j	1e-25, 2.11e-56j
0.146967048045329988 + 1.0140034082511197504e-193j	1.22e-23, 2.77e-54j
0.32166436151282999193 + 5.099213461659560229e-194j	1.8e-23, 3.23e-54j

Download

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