Rule: Q[18]

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.

$P_{1}$ :
$t^{18} - 153 \cdot t^{16} + 9180 \cdot t^{14} - 278460 \cdot t^{12} + 4594590 \cdot t^{10} - 41351310 \cdot t^{8} + 192972780 \cdot t^{6} - 413513100 \cdot t^{4} + 310134825 \cdot t^{2} - 34459425$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
6.0077459113595975203 + 1.6902671650219426907e-371j	1.54e-123, 1.54e-123j
-2.5958336889112403291 - 1.4167655711246174031e-378j	2.38e-124, 2.38e-124j
3.3747365357780909953 - 1.3792815404158086131e-385j	8.39e-124, 8.39e-124j
-7.1394648491464788756 - 1.3654952994330555037e-391j	4.06e-124, 4.06e-124j
-1.0983955180915012277 - 3.9014151412373014392e-391j	6.08e-126, 6.08e-126j
-4.1880202316294037045 + 7.0069417792182788469e-400j	1.67e-123, 1.67e-123j
5.0540726854427398454 - 3.1481879345887188604e-411j	2.28e-123, 2.28e-123j
7.1394648491464788756 + 1.3993985483394197474e-418j	4.15e-124, 4.15e-124j
-6.0077459113595975203 - 2.2292071916729186472e-418j	1.32e-123, 1.32e-123j
0.36524575550769759592 - 2.1882543641913301915e-422j	8.68e-127, 8.68e-127j
1.8397799215086454897 - 3.6049908847625187934e-437j	5.36e-125, 5.36e-125j
4.1880202316294037045 + 1.7890407554726829268e-450j	1.93e-123, 1.93e-123j
-0.36524575550769759592 + 6.8192109107598669961e-455j	8.68e-127, 8.68e-127j
-3.3747365357780909953 - 1.1637249879606152609e-455j	9.04e-124, 9.04e-124j
-5.0540726854427398454 + 2.5702892001904652192e-458j	2.15e-123, 2.15e-123j
1.0983955180915012277 + 5.1653054852742917063e-461j	6.08e-126, 6.08e-126j
2.5958336889112403291 - 3.2167035057683305849e-470j	2.71e-124, 2.71e-124j
-1.8397799215086454897 - 2.2564346707881541231e-485j	4.65e-125, 4.65e-125j

Weights

Weight (ball center)	Error (ball radius)
5.9054884788365959304e-09 - 2.9984089310368844615e-379j	7.7e-54, 9.89e-115j
0.010516517751941341968 + 1.5463125333919052033e-377j	2.84e-48, 3.64e-109j
0.0010654847962916520137 + 1.6102120343991328209e-377j	3.58e-50, 4.61e-111j
4.4165887693587052281e-12 - 2.0769864514875218139e-382j	5.63e-56, 7.23e-117j
0.16068530389351263536 + 7.3233014853787147706e-377j	4.34e-45, 5.58e-106j
5.1798961441162062137e-05 + 9.1756088043261724322e-379j	2.59e-52, 3.33e-113j
1.0215523976369812623e-06 + 1.3766005728102354119e-378j	1.87e-53, 2.4e-114j
4.4165887693587052281e-12 - 2.4120916981132225932e-381j	4.18e-56, 5.37e-117j
5.9054884788365959304e-09 + 8.3107585980444066394e-381j	2.54e-55, 3.26e-116j
0.27278323465428787436 + 1.2020649913470550629e-376j	1.27e-48, 1.63e-109j
0.054896632480222629647 + 7.3010665191135574565e-377j	8.25e-51, 1.06e-111j
5.1798961441162062137e-05 - 5.1371806706728653048e-378j	6.98e-53, 8.96e-114j
0.27278323465428787436 - 1.0641673808341602663e-376j	3.81e-49, 4.88e-110j
0.0010654847962916520137 - 4.5250553455806057701e-378j	1e-52, 1.28e-113j
1.0215523976369812623e-06 - 1.1874233871715233601e-379j	1.92e-54, 2.47e-115j
0.16068530389351263536 - 1.0604318346340810477e-376j	2.37e-51, 3.14e-112j
0.010516517751941341968 - 3.9038171931906294927e-377j	2.47e-52, 3.23e-113j
0.054896632480222629647 - 3.8736364552231505701e-377j	6.23e-52, 7.62e-113j

Download

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