Rule: Q[4, 5]

Type

This rule is of Hermite (physicists') 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.

$P_{1}$ :
$16 \cdot t^{4} - 48 \cdot t^{2} + 12$
$P_{2}$ :
$16 \cdot t^{9} - 168 \cdot t^{7} + 432 \cdot t^{5} - 270 \cdot t^{3} + 45 \cdot t$

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)
2.6384291054842239697 + 8.0614513290805065021e-137j	1.04e-62, 1.04e-62j
-1.6506801238857845559 - 1.0748601772107342003e-137j	1.42e-62, 1.42e-62j
-2.6384291054842239697 + 3.3169513281112500712e-138j	1.04e-62, 1.04e-62j
0.52464762327529031788 - 1.5048042480950278804e-136j	6.07e-63, 6.07e-63j
0.73395630342256598469 + 1.6794690268917721879e-139j	8.2e-63, 8.2e-63j
1.6506801238857845559 - 3.2033329522929614791e-145j	1.42e-62, 1.42e-62j
2.2227587494850774834e-161 - 3.889827811598885596e-162j	2.03e-160, 2.03e-160j
-0.73395630342256598469 + 1.882749894611628217e-183j	1.05e-62, 1.05e-62j
-0.52464762327529031788 + 3.4247021078256297496e-195j	6.07e-63, 6.07e-63j

Weights

Weight (ball center)	Error (ball radius)
0.00059220888055192656046 - 1.7079968786022462905e-139j	8.1e-30, 6.4e-61j
0.033742373970539285842 - 1.1311289364039448033e-138j	1.38e-28, 1.09e-59j
0.00059220888055192656046 - 1.2355462870605717217e-140j	3.66e-30, 2.89e-61j
-0.17742053489007951573 + 6.0888811858458961945e-137j	6.98e-27, 5.45e-58j
0.37641928537232163666 - 8.7295835219025796677e-137j	3.71e-27, 2.91e-58j
0.033742373970539285842 + 1.3243286384439017771e-138j	4.37e-29, 3.47e-60j
0.53333333333333333333 + 3.6885288943717795163e-137j	2.22e-27, 1.73e-58j
0.37641928537232163666 + 1.6531553136722653222e-137j	4.16e-28, 3.2e-59j
-0.17742053489007951573 - 2.701986327118274028e-137j	6.76e-28, 5.25e-59j

Download

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