Rule: Q[14]

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.

$P_{1}$ :
$16384 \cdot t^{14} - 745472 \cdot t^{12} + 12300288 \cdot t^{10} - 92252160 \cdot t^{8} + 322882560 \cdot t^{6} - 484323840 \cdot t^{4} + 242161920 \cdot t^{2} - 17297280$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.7484707249854025686 + 1.3555799241203723162e-181j	8.15e-61, 8.15e-61j
-4.3044485704736318126 - 5.0274846123815145565e-188j	2.78e-61, 2.78e-61j
4.3044485704736318126 + 5.0562130958808374968e-186j	2.78e-61, 2.78e-61j
3.4626569336022705502 - 8.9776510935384188508e-189j	9.7e-61, 9.7e-61j
0.87871378732939941611 - 8.767237396033612159e-193j	2.63e-62, 2.63e-62j
-1.4766827311411408706 + 1.8728839652171412693e-195j	1.41e-61, 1.41e-61j
-2.0951832585077168157 - 4.1805445652168331904e-197j	5.15e-61, 5.15e-61j
-2.7484707249854025686 - 2.0902722826084165952e-199j	8.23e-61, 8.23e-61j
-3.4626569336022705502 - 2.2177008766192087767e-204j	1.2e-60, 1.2e-60j
0.29174551067256207845 + 4.532555499780559119e-217j	1.97e-63, 1.97e-63j
1.4766827311411408706 + 1.3284869337294087448e-231j	1.41e-61, 1.41e-61j
2.0951832585077168157 + 2.6244694243173541709e-241j	4.45e-61, 4.45e-61j
-0.29174551067256207845 - 4.5400977764418515234e-243j	3.43e-63, 3.43e-63j
-0.87871378732939941611 + 1.7162668005702563722e-244j	2.47e-62, 2.47e-62j

Weights

Weight (ball center)	Error (ball radius)
0.00020033955376074414217 - 7.4641948206676156597e-185j	2.26e-20, 1.19e-50j
4.8681612577483808128e-09 + 1.8981131038765165631e-188j	1.01e-23, 5.29e-54j
4.8681612577483808128e-09 + 8.6037348880415420224e-188j	2.27e-23, 1.19e-53j
2.6609913440676305554e-06 - 4.3824672071558594719e-186j	5.57e-22, 2.92e-52j
0.15408333984251362572 + 4.0281089970113633867e-184j	8.44e-20, 4.43e-50j
0.03865010882425340019 + 8.9277375162424291567e-185j	7.98e-20, 4.19e-50j
0.0044289191069474034969 - 2.6362361089726573772e-185j	1.94e-21, 1.02e-51j
0.00020033955376074414217 + 4.9404986141553152508e-186j	7.07e-23, 3.72e-53j
2.6609913440676305554e-06 - 5.0391793534947243599e-187j	4.91e-24, 2.57e-54j
0.30263462681301950107 - 4.2964647835573934126e-184j	3.16e-21, 1.66e-51j
0.03865010882425340019 - 2.9659864108251254164e-184j	2.54e-22, 1.37e-52j
0.0044289191069474034969 + 1.9545782077034678411e-184j	5.05e-23, 2.71e-53j
0.30263462681301950107 + 3.4718693142348041133e-184j	5.73e-22, 3.01e-52j
0.15408333984251362572 - 2.0764273027430237634e-184j	4.61e-22, 2.06e-52j

Download

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