Rule: Q[13]

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.

$P_{1}$ :
$8192 \cdot t^{13} - 319488 \cdot t^{11} + 4392960 \cdot t^{9} - 26357760 \cdot t^{7} + 69189120 \cdot t^{5} - 69189120 \cdot t^{3} + 17297280 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-3.2466089783724099881 - 1.251604045410300778e-308j	7.15e-125, 7.15e-125j
-0.60576387917106011308 + 2.7813423231340017289e-309j	7.6e-127, 7.6e-127j
-4.1013375961786396412 + 2.444539151191993707e-311j	2.84e-125, 2.84e-125j
-1.2200550365907484262 - 6.518771069845316552e-311j	7.97e-126, 7.97e-126j
-1.853107651601512142 - 7.0829250987801104573e-320j	3.23e-125, 3.23e-125j
-2.5197356856782378834 + 9.8083565656408691186e-347j	1.08e-124, 1.08e-124j
1.853107651601512142 - 1.0564169781387141817e-373j	2.97e-125, 2.97e-125j
2.5197356856782378834 - 3.6651826647954097925e-390j	8.87e-125, 8.87e-125j
3.2466089783724099881 + 1.1333778329848785956e-401j	7.9e-125, 7.9e-125j
4.1013375961786396412 + 1.8334053180637741988e-402j	4.1e-125, 4.1e-125j
0.60576387917106011308 + 6.9541482635229389187e-410j	7.6e-127, 7.6e-127j
1.2200550365907484262 + 5.6471080366227875911e-424j	8.42e-126, 8.42e-126j
1.0939300727262532515e-430 + 7.3629908741190122697e-432j	1.43e-429, 1.43e-429j

Weights

Weight (ball center)	Error (ball radius)
1.1526596527333874013e-05 - 2.2430708064665663434e-312j	2.68e-51, 3.22e-114j
0.23787152296413627089 + 4.0748899217909496171e-310j	6.21e-48, 7.45e-111j
2.7226276428059033082e-08 + 5.6882548853752783048e-314j	1.11e-52, 1.33e-115j
0.079168955860450007974 + 6.20943034736856113e-310j	6.07e-48, 7.29e-111j
0.011770560505996535835 - 1.2444000563104790992e-310j	1.22e-49, 1.46e-112j
0.00068123635044292719588 + 2.0392855237302389078e-311j	1.36e-50, 1.64e-113j
0.011770560505996535835 + 5.9596789612289578725e-311j	4.04e-52, 4.85e-115j
0.00068123635044292719588 - 1.1263705466813952904e-311j	1.31e-53, 1.57e-116j
1.1526596527333874013e-05 + 1.1872168886087408576e-312j	4.57e-55, 5.49e-118j
2.7226276428059033082e-08 - 4.7166163350919282258e-314j	1.65e-56, 1.97e-119j
0.23787152296413627089 + 5.4560853437778507097e-310j	2.01e-52, 2.41e-115j
0.079168955860450007974 - 2.0848573332665277086e-310j	8.27e-53, 1.04e-115j
0.34099234099234099234 - 1.3087946241864584878e-309j	2.57e-52, 2.9e-115j

Download

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