Rule: Q[3, 8]

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.

$P_{1}$ :
$t^{3} - 3 \cdot t$
$P_{2}$ :
$t^{11} - \frac{149}{3} \cdot t^{9} + 798 \cdot t^{7} - 4914 \cdot t^{5} + 10605 \cdot t^{3} - 5355 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.6840395601585691766 + 8.6826513651760839197e-165j	1.64e-61, 1.64e-61j
4.9791465117195582423 - 2.1197879309511923632e-168j	1.26e-61, 1.26e-61j
-1.7320508075688772935 - 9.2540922819950750121e-179j	5.51e-62, 5.51e-62j
-2.6840395601585691766 - 3.2990979579943574951e-196j	1.61e-61, 1.61e-61j
3.7355715460409572598 - 5.9932286886948520618e-195j	2.59e-61, 2.59e-61j
-4.9791465117195582423 - 1.0451361413042082976e-199j	1.26e-61, 1.26e-61j
-3.9868779804390270142e-205 + 3.9868779804390270142e-205j	6.2e-204, 6.2e-204j
-0.84628809835102169611 - 7.4261389308404680606e-214j	5.47e-63, 5.47e-63j
-3.7355715460409572598 - 4.3225817678266135397e-224j	2.84e-61, 2.84e-61j
1.7320508075688772935 - 4.2212712576431772849e-226j	5.17e-62, 5.17e-62j
0.84628809835102169611 + 0j	8.41e-63, 8.41e-63j

Weights

Weight (ball center)	Error (ball radius)
0.010812729181550774617 - 1.4671127475688891288e-166j	6.77e-24, 1.96e-54j
2.3417977747018329504e-06 + 3.8492060251775705022e-169j	1.01e-26, 2.93e-57j
0.081442699243746364165 + 7.2128210324439781738e-167j	2.54e-23, 7.36e-54j
0.010812729181550774617 - 1.748908429432839921e-167j	3.56e-25, 1.03e-55j
0.00041751146352803366757 - 1.4069065051413826082e-167j	3.42e-26, 9.93e-57j
2.3417977747018329504e-06 - 1.1527840396493827976e-169j	2.61e-28, 7.56e-59j
0.33464052287581699346 + 3.0476204180169475694e-166j	1.77e-24, 4.99e-55j
0.24000445687549162899 - 1.8342462724942125786e-166j	9.95e-25, 2.82e-55j
0.00041751146352803366757 + 2.3044916796095177056e-168j	5.75e-27, 1.67e-57j
0.081442699243746364165 + 3.3458940245633694378e-166j	1.12e-25, 3.3e-56j
0.24000445687549162899 - 3.523597371085814229e-166j	4.13e-25, 1.12e-55j

Download

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