Rule: Q[2, 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.

$P_{1}$ :
$4 \cdot t^{2} - 2$
$P_{2}$ :
$4 \cdot t^{7} - \frac{106}{3} \cdot t^{5} + \frac{215}{3} \cdot t^{3} - \frac{55}{2} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.7071067811865475244 + 9.3612369786833883226e-106j	5.38e-63, 5.38e-63j
-2.4631197782145911371 - 9.2942205956383638548e-120j	1.49e-62, 1.49e-62j
-1.5054482028623358456 - 1.1541223272232169726e-128j	2.02e-62, 2.02e-62j
2.4631197782145911371 + 8.5988814176858736023e-137j	1.71e-62, 1.71e-62j
-2.5626663618343691833e-144 + 9.6099988568788844373e-145j	1.92e-143, 1.92e-143j
1.5054482028623358456 - 2.8640028407808793894e-152j	1.89e-62, 1.89e-62j
-0.7071067811865475244 - 5.6902623986817983576e-160j	4.47e-63, 4.47e-63j

Weights

Weight (ball center)	Error (ball radius)
0.25423728813559322034 - 2.5386070633366643259e-106j	1.61e-27, 7.55e-59j
0.001428811839066749964 - 2.8755004634469268581e-108j	4.46e-29, 2.15e-60j
0.050394506085946090303 + 3.476036984275289199e-107j	6.69e-28, 3.23e-59j
0.001428811839066749964 + 5.1912986727421275775e-108j	6.87e-30, 3.32e-61j
0.38787878787878787879 + 4.8141048348518506814e-106j	5.93e-28, 2.78e-59j
0.050394506085946090303 - 9.6336263476754024417e-107j	5.64e-29, 2.74e-60j
0.25423728813559322034 - 1.6828968172681270384e-106j	2.36e-28, 1.02e-59j

Download

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