Rule: Q[13]

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.

$P_{1}$ :
$t^{13} - 78 \cdot t^{11} + 2145 \cdot t^{9} - 25740 \cdot t^{7} + 135135 \cdot t^{5} - 270270 \cdot t^{3} + 135135 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
4.5913984489365206271 + 4.017397398342840147e-133j	9.39e-61, 9.39e-61j
-5.8001672523865003059 + 2.2840778765728101756e-137j	3.11e-61, 3.11e-61j
-4.5913984489365206271 + 9.3847645086707855833e-148j	9.39e-61, 9.39e-61j
2.6206899734322147806 + 1.2859993021020864288e-157j	2.61e-61, 2.61e-61j
-3.5634443802816340916 + 6.104989241139434006e-166j	9.85e-61, 9.85e-61j
3.5634443802816340916 + 9.3154743059378570649e-171j	7.75e-61, 7.75e-61j
5.8001672523865003059 + 2.7145337360518886702e-177j	3.42e-61, 3.42e-61j
-0.8566794935194500339 + 1.0543399409825118015e-181j	8.2e-63, 8.2e-63j
-2.6206899734322147806 + 1.3495551244576151059e-179j	2.64e-61, 2.64e-61j
0.8566794935194500339 + 8.2370307889258734493e-184j	9.48e-63, 9.48e-63j
1.7254183795882391615 - 3.0299572440692163622e-189j	8.71e-62, 8.71e-62j
4.3836186980168060795e-193 + 7.0137899168268897272e-192j	9.14e-191, 9.14e-191j
-1.7254183795882391615 + 5.4795233725210075994e-194j	6.21e-62, 6.21e-62j

Weights

Weight (ball center)	Error (ball radius)
1.1526596527333874013e-05 - 1.0630677012106050706e-137j	9.36e-26, 3.21e-56j
2.7226276428059033082e-08 + 2.1659311136523532587e-140j	2.77e-27, 9.51e-58j
1.1526596527333874013e-05 - 5.0428961309699840423e-139j	3.27e-26, 1.12e-56j
0.011770560505996535835 - 7.5088219824503822292e-137j	1.49e-24, 5.12e-55j
0.00068123635044292719588 + 4.3654902901850504029e-138j	1.18e-25, 4.06e-56j
0.00068123635044292719588 + 3.4631449433991235097e-137j	7.25e-26, 2.49e-56j
2.7226276428059033082e-08 - 1.8618560337518418095e-139j	2.47e-28, 8.46e-59j
0.23787152296413627089 - 1.2210250580851883559e-136j	1.71e-24, 6.63e-55j
0.011770560505996535835 - 2.0518026728340525054e-137j	1.12e-25, 3.86e-56j
0.23787152296413627089 - 1.7811861670390275092e-136j	7.39e-25, 2.88e-55j
0.079168955860450007974 + 1.3390601613884725832e-136j	4.16e-25, 1.56e-55j
0.34099234099234099234 + 1.734696965376815375e-136j	3.81e-25, 1.67e-55j
0.079168955860450007974 + 6.0754209582002562303e-137j	2.97e-25, 9.26e-56j

Download

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