Rule: Q[2, 5]

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.

$P_{1}$ :
$t^{2} - 1$
$P_{2}$ :
$t^{7} - \frac{53}{3} \cdot t^{5} + \frac{215}{3} \cdot t^{3} - 55 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
3.4833773961004847262 + 5.3743008860536710014e-138j	2.46e-62, 2.46e-62j
-2.1290252659381178426 + 1.0496681418073576175e-140j	2.34e-62, 2.34e-62j
-1 - 9.6099988568788844373e-145j	6.07e-63, 6.07e-63j
-3.4833773961004847262 - 2.237502219360062023e-154j	2.46e-62, 2.46e-62j
2.1290252659381178426 + 1.9407238137370535552e-172j	2.34e-62, 2.34e-62j
1 + 9.1931147197833409032e-187j	6.07e-63, 6.07e-63j
-1.6053291130432639451e-196 - 8.561755269564074374e-196j	6.1e-195, 6.1e-195j

Weights

Weight (ball center)	Error (ball radius)
0.001428811839066749964 - 1.5160631821560604128e-140j	2.08e-30, 1.5e-61j
0.050394506085946090303 + 1.2256985186481955869e-140j	1.56e-29, 1.13e-60j
0.25423728813559322034 - 4.6165786959535514296e-140j	7.82e-29, 5.58e-60j
0.001428811839066749964 - 1.0559172300988110028e-141j	8.2e-31, 5.97e-62j
0.050394506085946090303 + 4.795863371371769077e-140j	7.4e-30, 5.05e-61j
0.25423728813559322034 - 8.1251050209617014206e-140j	3.15e-29, 1.99e-60j
0.38787878787878787879 + 8.3417767320612296993e-140j	2.48e-29, 2.03e-60j

Download

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