Rule: Q[18]

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.

$P_{1}$ :
$262144 \cdot t^{18} - 20054016 \cdot t^{16} + 601620480 \cdot t^{14} - 9124577280 \cdot t^{12} + 75277762560 \cdot t^{10} - 338749931520 \cdot t^{8} + 790416506880 \cdot t^{6} - 846874828800 \cdot t^{4} + 317578060800 \cdot t^{2} - 17643225600$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.3862990891666860003 + 1.0614691609870531223e-325j	5.3e-124, 5.3e-124j
-4.248117873568126463 + 1.3617105043134083894e-331j	9.31e-124, 9.31e-124j
-5.0483640088744667684 + 9.1442742749398959622e-333j	2.74e-124, 2.74e-124j
2.9613775055316068448 + 4.1527137660582084779e-330j	9.74e-124, 9.74e-124j
5.0483640088744667684 - 3.5316108417496680505e-334j	2.76e-124, 2.76e-124j
1.8355316042616288923 + 2.0274675935394992915e-332j	1.75e-124, 1.75e-124j
0.25826775051909675926 - 6.9662428072534766777e-338j	4.49e-127, 4.49e-127j
-0.77668291926741166132 - 1.716143116546864307e-349j	5.87e-126, 5.87e-126j
0.77668291926741166132 - 5.4808463336755721561e-355j	4.29e-126, 4.29e-126j
3.5737690684862660795 - 3.2290888484569317699e-359j	1.63e-123, 1.63e-123j
-1.3009208583896173657 - 1.0141602990131656144e-371j	3.99e-125, 3.99e-125j
-3.5737690684862660795 - 3.6168450846843566059e-377j	1.4e-123, 1.4e-123j
-0.25826775051909675926 - 1.5943544591860032597e-389j	4.49e-127, 4.49e-127j
-2.3862990891666860003 + 3.9254874591852736299e-398j	6.38e-124, 6.38e-124j
4.248117873568126463 + 7.8779134760552797603e-404j	1.01e-123, 1.01e-123j
-2.9613775055316068448 - 2.0981658760800638566e-407j	1.4e-123, 1.4e-123j
1.3009208583896173657 + 1.1565277259003468987e-420j	3.18e-125, 3.18e-125j
-1.8355316042616288923 - 7.4231464479283865242e-437j	1.65e-124, 1.65e-124j

Weights

Weight (ball center)	Error (ball radius)
0.0010654847962916520137 - 2.698839028046171093e-328j	2.82e-48, 2.33e-109j
5.9054884788365959304e-09 - 4.0133070823815389597e-332j	6.58e-53, 5.43e-114j
4.4165887693587052281e-12 + 9.7939853881323487217e-334j	3.46e-54, 2.85e-115j
5.1798961441162062137e-05 - 4.3363139182357403334e-329j	6.75e-51, 5.57e-112j
4.4165887693587052281e-12 + 2.735274110916971313e-333j	1.68e-55, 1.39e-116j
0.010516517751941341968 + 6.4512905162800401562e-328j	2.64e-49, 2.18e-110j
0.27278323465428787436 - 8.5037116658731719624e-328j	2.72e-48, 2.25e-109j
0.16068530389351263536 - 4.3910550370536452516e-328j	1.12e-48, 9.22e-110j
0.16068530389351263536 + 8.628664953095539522e-328j	1.2e-48, 9.94e-110j
1.0215523976369812623e-06 + 2.9490439994296358757e-330j	1.25e-52, 1.03e-113j
0.054896632480222629647 + 2.2016651513046238647e-328j	1.11e-49, 9.15e-111j
1.0215523976369812623e-06 + 5.8756564106885402081e-331j	2.58e-54, 2.13e-115j
0.27278323465428787436 + 6.8427691992977429497e-328j	6.14e-50, 5.02e-111j
0.0010654847962916520137 + 2.3697150436214784996e-329j	4.24e-53, 3.48e-114j
5.9054884788365959304e-09 - 1.4300983110757123586e-331j	1.58e-55, 1.32e-116j
5.1798961441162062137e-05 - 4.663078452665251652e-330j	6.46e-54, 5.38e-115j
0.054896632480222629647 - 7.4794519561634672869e-328j	4.86e-52, 4.99e-113j
0.010516517751941341968 - 8.4161327496558053359e-329j	1.3e-52, 1e-113j

Download

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