Rule: Q[26]

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.

$P_{1}$ :
$67108864 \cdot t^{26} - 10905190400 \cdot t^{24} + 752458137600 \cdot t^{22} - 28969638297600 \cdot t^{20} + 688028909568000 \cdot t^{18} - 10526842316390400 \cdot t^{16} + 105268423163904000 \cdot t^{14} - 684244750565376000 \cdot t^{12} + 2822509596082176000 \cdot t^{10} - 7056273990205440000 \cdot t^{8} + 9878783586287616000 \cdot t^{6} - 6735534263377920000 \cdot t^{4} + 1683883565844480000 \cdot t^{2} - 64764752532480000$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
5.5645249819501030972 - 8.5764296649320882624e-462j	3.9e-122, 3.9e-122j
-4.3796026629833049719 - 9.3835719532767531082e-464j	1.85e-121, 1.85e-121j
6.3095503856256935009 + 2.4916324567530696825e-477j	7.22e-123, 7.22e-123j
-3.8562884199091490218 + 1.5139222141621077812e-475j	1.66e-121, 1.66e-121j
3.3594271823508301366 + 6.3235080218923996764e-482j	1.08e-121, 1.08e-121j
3.8562884199091490218 + 1.0393670028819777304e-482j	1.55e-121, 1.55e-121j
-3.3594271823508301366 + 4.0951458006967126266e-482j	9.22e-122, 9.22e-122j
4.9413249572413790738 - 9.2831329522999815774e-489j	1.08e-121, 1.08e-121j
-1.5213615166519213667 - 1.5112675099424292543e-491j	5.46e-124, 5.46e-124j
4.3796026629833049719 + 2.8375674339458764728e-490j	2.1e-121, 2.1e-121j
1.0827330110778833562 - 6.098653492532141572e-493j	6.41e-125, 6.41e-125j
-5.5645249819501030972 - 7.5112079133861436046e-490j	4.53e-122, 4.53e-122j
-2.8817622195430872175 - 3.6175172974557566748e-496j	4.24e-122, 4.24e-122j
1.5213615166519213667 - 3.5774528733601760222e-500j	6.03e-124, 6.03e-124j
2.4184157647737791478 + 2.3057818466466027017e-499j	1.32e-122, 1.32e-122j
2.8817622195430872175 - 1.8696197829544973698e-499j	4.06e-122, 4.06e-122j
0.64809521399344830968 + 1.0196874791406886929e-502j	6.23e-126, 6.23e-126j
-2.4184157647737791478 - 6.0474027297847528536e-499j	1.2e-122, 1.2e-122j
-1.0827330110778833562 + 1.3676295531897441623e-503j	8.3e-125, 8.3e-125j
-0.21577785624346343465 + 4.2390506171622207195e-506j	5.6e-127, 5.6e-127j
-6.3095503856256935009 - 2.0407888653861884118e-501j	6.72e-123, 6.72e-123j
1.9658547856411365752 + 6.234607654252737099e-508j	3.22e-123, 3.22e-123j
0.21577785624346343465 - 1.0468913530012263985e-513j	5.6e-127, 5.6e-127j
-4.9413249572413790738 - 8.0618772834132860247e-515j	9.68e-122, 9.68e-122j
-0.64809521399344830968 + 6.2166354678741421889e-528j	6.23e-126, 6.23e-126j
-1.9658547856411365752 - 1.5608963205853775625e-526j	3.59e-123, 3.59e-123j

Weights

Weight (ball center)	Error (ball radius)
1.3445476496635730192e-14 + 6.8296287820745062864e-475j	7.12e-48, 1.73e-107j
1.4242932379880092971e-09 - 5.8910628379529604201e-472j	3.89e-46, 9.47e-106j
2.4806942603936308147e-18 + 1.5805663427633711036e-477j	1.96e-49, 4.77e-109j
9.986755573314586608e-08 + 2.1719002631746000712e-471j	5.21e-45, 1.27e-104j
3.4434136123081268523e-06 + 1.6860099821088485746e-471j	5.01e-44, 1.22e-103j
9.986755573314586608e-08 - 3.198593779904600639e-472j	2.6e-45, 6.33e-105j
3.4434136123081268523e-06 - 6.6483000447584826534e-471j	1.5e-45, 3.66e-105j
8.2428094431638531144e-12 - 5.6722726397224146436e-474j	7.9e-48, 1.93e-107j
0.024597665657121181035 - 2.1633070254415441703e-469j	4.34e-41, 1.06e-100j
1.4242932379880092971e-09 + 4.6932298180450111431e-473j	8.62e-47, 2.1e-106j
0.076229532206303023682 - 2.4026310839566946559e-469j	1.05e-39, 2.57e-99j
1.3445476496635730192e-14 + 3.3618862026034725414e-475j	6.44e-52, 1.57e-111j
6.5575586943338403451e-05 + 2.009925064217551159e-470j	5.21e-46, 1.27e-105j
0.024597665657121181035 + 1.3269842912797855544e-469j	1.44e-42, 3.5e-102j
0.00074420257636043386484 + 2.2834372263834314266e-470j	7.74e-45, 1.88e-104j
6.5575586943338403451e-05 - 6.9511172243421570806e-471j	2.09e-45, 5.09e-105j
0.16058654561379458559 + 3.6332122609404117862e-469j	9.68e-43, 2.36e-102j
0.00074420257636043386484 - 5.2658432057650615293e-470j	3.5e-46, 8.53e-106j
0.076229532206303023682 + 3.3787641587004316739e-469j	8.14e-44, 1.98e-103j
0.23247073563007765645 + 4.9302375655097521821e-469j	1.54e-43, 3.75e-103j
2.4806942603936308147e-18 - 2.7581629170473501633e-477j	2.25e-54, 5.49e-114j
0.0053021980156822443106 - 6.0760492461805688094e-470j	1.34e-45, 3.26e-105j
0.23247073563007765645 - 4.6120650594644533788e-469j	5.16e-45, 1.29e-104j
8.2428094431638531144e-12 - 1.7828450704896504781e-473j	3.71e-51, 9.04e-111j
0.16058654561379458559 - 4.4445707565073885178e-469j	1.33e-45, 3.42e-105j
0.0053021980156822443106 + 1.1644888964428165265e-469j	1.37e-46, 3.28e-106j

Download

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