Rule: Q[1, 20]

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.

$P_{1}$ :
$t$
$P_{2}$ :
$t^{21} - 210 \cdot t^{19} + 17955 \cdot t^{17} - 813960 \cdot t^{15} + 21366450 \cdot t^{13} - 333316620 \cdot t^{11} + 3055402350 \cdot t^{9} - 15713497800 \cdot t^{7} + 41247931725 \cdot t^{5} - 45831035250 \cdot t^{3} + 13749310575 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
7.849382895113821993 - 1.4112283860720260906e-347j	1.77e-123, 1.77e-123j
-2.0491024682571626618 - 2.8831535401105874363e-354j	1.25e-124, 1.25e-124j
-5.8293820073044713717 - 5.5712422367483463497e-355j	1.21e-122, 1.21e-122j
-7.849382895113821993 - 5.9842682544065152801e-358j	2.22e-123, 2.22e-123j
4.21434398168842135 + 1.0448696137527770763e-364j	9.07e-123, 9.07e-123j
2.7505929810523730936 + 1.7156145587837163865e-381j	9.76e-124, 9.76e-124j
6.7514447187174607668 + 4.2668341947666017717e-400j	8.22e-123, 8.22e-123j
-2.7505929810523730936 - 1.1599678255516571212e-404j	7.97e-124, 7.97e-124j
-1.3597658232112302657 - 3.3454420396304995441e-408j	2.03e-125, 2.03e-125j
-4.21434398168842135 + 8.2400696224235235096e-406j	8.03e-123, 8.03e-123j
2.0491024682571626618 + 5.3273742947345371359e-409j	1.68e-124, 1.68e-124j
-4.9949639447820251929 + 5.0665937348524269265e-409j	1.15e-122, 1.15e-122j
-6.7514447187174607668 - 6.9738621871790917989e-418j	8.22e-123, 8.22e-123j
5.8293820073044713717 + 1.7734457745169486558e-426j	1.21e-122, 1.21e-122j
-3.4698466904753762952 - 1.0457608340493706691e-436j	3.49e-123, 3.49e-123j
1.3597658232112302657 + 1.7378407145567142227e-438j	2.06e-125, 2.06e-125j
3.4698466904753762952 - 6.2964888347312743328e-439j	3.27e-123, 3.27e-123j
4.9949639447820251929 + 1.8184562428692978656e-454j	1.22e-122, 1.22e-122j
-0.67804569244064402621 - 1.1573177586158923445e-466j	1.71e-126, 1.71e-126j
-6.9834729707933332923e-467 + 3.6005441379161095162e-466j	7.7e-465, 7.7e-465j
0.67804569244064402621 + 3.0218852586081633439e-467j	1.71e-126, 1.71e-126j

Weights

Weight (ball center)	Error (ball radius)
2.0989912195656767434e-14 + 1.1703298569638742023e-360j	1.11e-48, 1.67e-110j
0.033952729786542835053 - 1.3835121882392849037e-355j	1.46e-37, 2.2e-99j
1.4506612844930866107e-08 + 1.0528039193670355567e-360j	1.35e-46, 2.03e-108j
2.0989912195656767434e-14 + 5.6038213348999728825e-363j	3.07e-49, 4.62e-111j
4.2192347425516757386e-05 + 4.2044128361732766634e-357j	4.52e-45, 6.8e-107j
0.0064396970514087768692 + 4.1060325455267248075e-356j	2.42e-42, 3.64e-104j
4.9753686041217240051e-11 - 1.3560984982461297974e-359j	1.84e-48, 2.77e-110j
0.0064396970514087768692 - 4.5296942689573065143e-356j	9.31e-43, 1.4e-104j
0.10839228562641944345 + 3.2681981092020047921e-355j	1.55e-39, 2.34e-101j
4.2192347425516757386e-05 - 4.9312819437519044706e-358j	7.92e-46, 1.19e-107j
0.033952729786542835053 - 8.8836493085770794358e-356j	3.46e-43, 5.2e-105j
1.2253548361482535298e-06 + 2.351172815468150817e-359j	5.67e-47, 8.53e-109j
4.9753686041217240051e-11 - 1.9134281450230700151e-361j	2.34e-49, 3.51e-111j
1.4506612844930866107e-08 + 1.3002950035020675255e-358j	1.46e-49, 2.2e-111j
0.00070804779548153646931 + 5.1443296459802441106e-357j	6.5e-46, 9.77e-108j
0.10839228562641944345 + 1.5503081978633923322e-355j	4.77e-45, 7.16e-107j
0.00070804779548153646931 - 1.4983631145022126413e-356j	2.89e-47, 4.35e-109j
1.2253548361482535298e-06 - 8.7637421843122299952e-358j	8.52e-49, 1.28e-110j
0.2153337156950596866 - 2.910609640914945249e-355j	4.37e-45, 6.67e-107j
0.27026018357287707133 + 2.7018850180013660861e-355j	2.63e-45, 4.11e-107j
0.2153337156950596866 - 2.2269146583380726572e-355j	1.28e-45, 1.8e-107j

Download

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