Rule: Q[24]

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.

$P_{1}$ :
$16777216 \cdot t^{24} - 2315255808 \cdot t^{22} + 133706022912 \cdot t^{20} - 4234024058880 \cdot t^{18} + 80975710126080 \cdot t^{16} - 971708521512960 \cdot t^{14} + 7368789621473280 \cdot t^{12} - 34738579644088320 \cdot t^{10} + 97702255248998400 \cdot t^{8} - 151981285942886400 \cdot t^{6} + 113985964457164800 \cdot t^{4} - 31087081215590400 \cdot t^{2} + 1295295050649600$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
4.625662756423787265 + 5.9851286172692635599e-482j	4.41e-122, 4.41e-122j
-4.0536644024481495039 + 6.0036250273038402927e-487j	5.45e-122, 5.45e-122j
-6.0159255614257397173 + 3.9700176714898061448e-493j	3.81e-123, 3.81e-123j
-3.5200068130345247113 - 2.451423208381747723e-498j	5.5e-122, 5.5e-122j
6.0159255614257397173 + 7.0916278225678027934e-504j	3.28e-123, 3.28e-123j
4.0536644024481495039 + 6.0491038832803307513e-503j	6.28e-122, 6.28e-122j
2.5238810170114269742 + 3.6555850195187418021e-505j	8.57e-123, 8.57e-123j
-3.0125461375655648257 + 6.8662298298116370442e-509j	1.96e-122, 1.96e-122j
-4.625662756423787265 - 1.9167500821400662329e-519j	4.74e-122, 4.74e-122j
3.5200068130345247113 + 6.6466976909474900385e-522j	4.01e-122, 4.01e-122j
1.5842500109616941485 + 4.9359902871710524814e-528j	3.47e-124, 3.47e-124j
3.0125461375655648257 + 2.7403017628575192996e-526j	2.13e-122, 2.13e-122j
-2.5238810170114269742 - 3.2855305574778478715e-528j	8.7e-123, 8.7e-123j
0.674171107037212236 - 1.5988814615822434623e-535j	5.41e-126, 5.41e-126j
-0.22441454747251558515 - 1.3569567657099929277e-535j	5.75e-127, 5.75e-127j
1.1267608176112450721 + 5.7007089472835528826e-535j	6.46e-125, 6.46e-125j
5.2593829276680443674 - 7.0510550920147730725e-531j	2.03e-122, 2.03e-122j
-2.0490035736616989118 - 3.6161665251441156692e-532j	2.34e-123, 2.34e-123j
-1.1267608176112450721 + 1.1513322398439767624e-533j	6.08e-125, 6.08e-125j
2.0490035736616989118 - 1.0745584121870767823e-534j	2.21e-123, 2.21e-123j
-5.2593829276680443674 + 1.659940395580066173e-537j	2.23e-122, 2.23e-122j
0.22441454747251558515 + 1.6053999944110540592e-545j	5.75e-127, 5.75e-127j
-1.5842500109616941485 - 1.2872231300022118132e-546j	4.52e-124, 4.52e-124j
-0.674171107037212236 - 6.8764225861722541608e-551j	6.07e-126, 6.07e-126j

Weights

Weight (ball center)	Error (ball radius)
1.7186649279648580221e-10 - 4.7581422575403076988e-491j	5.44e-48, 2.24e-108j
2.2674616734806419913e-08 - 1.3557791457346779227e-491j	5.2e-47, 2.14e-107j
9.3901936890419560729e-17 + 7.1494262945793571724e-496j	2.64e-51, 1.08e-111j
1.2176597454425813213e-06 + 1.0610621864617073354e-490j	7.11e-46, 2.93e-106j
9.3901936890419560729e-17 + 5.4691064276764065484e-495j	5.36e-52, 2.2e-112j
2.2674616734806419913e-08 + 2.0655740221273359621e-490j	2.92e-48, 1.2e-108j
0.00046471871877939570042 - 8.0474923798717373286e-489j	1.88e-45, 7.75e-106j
3.2095005652745912496e-05 - 5.814723009232143539e-490j	1.47e-46, 6.04e-107j
1.7186649279648580221e-10 + 1.1139591984186327654e-492j	1.01e-49, 4.15e-110j
1.2176597454425813213e-06 - 7.8307752526398606516e-490j	5.52e-48, 2.27e-108j
0.021126344408967546632 - 3.7495479944699752012e-488j	1.3e-44, 5.35e-105j
3.2095005652745912496e-05 + 2.7555648395412395271e-489j	2.83e-47, 1.17e-107j
0.00046471871877939570042 + 2.3645686659020411649e-489j	1.56e-47, 6.43e-108j
0.16145951286700008649 - 7.9780732978787091618e-488j	7.58e-45, 3.1e-105j
0.24087011554664032552 - 7.9386839554838380609e-488j	2.93e-45, 1.2e-105j
0.072069364017178329609 + 6.0197557663323696217e-488j	3.81e-45, 1.56e-105j
3.7149741527623985404e-13 - 7.546626688538606586e-493j	7.57e-52, 3.12e-112j
0.0039766089291813086419 - 7.4101899365828552167e-489j	2.25e-47, 9.26e-108j
0.072069364017178329609 - 3.6609620645972897187e-488j	2.16e-46, 8.89e-107j
0.0039766089291813086419 + 1.9202042711429031196e-488j	9.23e-47, 3.77e-107j
3.7149741527623985404e-13 - 4.8425972671297828195e-494j	1.1e-52, 4.5e-113j
0.24087011554664032552 + 8.7484922715377736618e-488j	3.3e-46, 1.35e-106j
0.021126344408967546632 + 1.8359883584874593583e-488j	1.63e-47, 6.86e-108j
0.16145951286700008649 + 5.9478523625059471002e-488j	4.95e-47, 1.86e-107j

Download

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