Rule: Q[22]

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.

$P_{1}$ :
$4194304 \cdot t^{22} - 484442112 \cdot t^{20} + 23011000320 \cdot t^{18} - 586780508160 \cdot t^{16} + 8801707622400 \cdot t^{14} - 80095539363840 \cdot t^{12} + 440525466501120 \cdot t^{10} - 1415974713753600 \cdot t^{8} + 2477955749068800 \cdot t^{6} - 2064963124224000 \cdot t^{4} + 619488937267200 \cdot t^{2} - 28158588057600$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-2.1442335927985344636 + 6.0200238460546893993e-381j	1.49e-123, 1.49e-123j
3.165265909202137447 - 3.3320739750570835733e-382j	1.12e-122, 1.12e-122j
4.9398341310601758879 - 2.0570848848319538438e-382j	6.76e-123, 6.76e-123j
3.7107015328778049148 + 8.2237081558696572588e-384j	1.43e-122, 1.43e-122j
4.2943124805931615158 - 1.3145022223543749895e-383j	1.49e-122, 1.49e-122j
-5.7092013532052637774 - 2.2252258726159762271e-382j	1.76e-123, 1.76e-123j
-1.1767139584812444474 + 6.3756585490649112422e-386j	5e-125, 5e-125j
-4.2943124805931615158 - 1.3745901066048704886e-386j	1.28e-122, 1.28e-122j
-3.165265909202137447 + 1.1733166005676305598e-388j	1.18e-122, 1.18e-122j
-4.9398341310601758879 + 4.2503949359810050084e-393j	8.23e-123, 8.23e-123j
-3.7107015328778049148 + 4.2320441354761528075e-394j	1.73e-122, 1.73e-122j
1.1767139584812444474 - 1.4661909001766735338e-398j	4.43e-125, 4.43e-125j
2.6456374410581727008 - 2.6558288046029639076e-412j	5.44e-123, 5.44e-123j
-0.2341791399309906351 + 5.2182530992623652067e-416j	3.31e-127, 3.31e-127j
5.7092013532052637774 + 5.082397232960508832e-423j	1.65e-123, 1.65e-123j
0.2341791399309906351 + 4.5494514120042332531e-422j	3.31e-127, 3.31e-127j
2.1442335927985344636 - 5.6379472978968436808e-429j	1.66e-123, 1.66e-123j
-1.6558743732864224954 - 8.0327272092090786759e-432j	2.93e-124, 2.93e-124j
-0.70368609717000693217 - 1.4614319569359010969e-436j	5.86e-126, 5.86e-126j
-2.6456374410581727008 + 4.9072693514557724404e-440j	5.01e-123, 5.01e-123j
1.6558743732864224954 + 4.4936735100610658905e-445j	2.99e-124, 2.99e-124j
0.70368609717000693217 - 1.5144835845531301525e-448j	5.86e-126, 5.86e-126j

Weights

Weight (ball center)	Error (ball radius)
0.0028087610475772157675 + 3.6243334841330640631e-383j	5.48e-37, 2.67e-98j
1.3345977126809514312e-05 - 2.0542673132303834133e-385j	7.24e-41, 3.53e-102j
9.8413789823460859326e-12 + 1.4347275823382643567e-388j	2.72e-45, 1.33e-106j
3.3198537498140360617e-07 + 3.2674612388717844442e-386j	8.05e-43, 3.93e-104j
3.3665141594582111065e-09 - 2.9382036868878157927e-387j	4.51e-44, 2.2e-105j
3.4794606478771458294e-15 - 5.2873934231267802242e-390j	1.67e-49, 8.14e-111j
0.067196311428890026671 + 8.5412899343388331189e-383j	5.7e-38, 2.78e-99j
3.3665141594582111065e-09 - 8.619579699497571756e-387j	2.22e-47, 1.08e-108j
1.3345977126809514312e-05 - 1.1422759028565340288e-384j	1.5e-45, 7.29e-107j
9.8413789823460859326e-12 + 3.5850772609471267215e-388j	9.18e-49, 4.48e-110j
3.3198537498140360617e-07 + 1.1745897808271778837e-385j	1.01e-46, 4.92e-108j
0.067196311428890026671 - 2.4746474473117032765e-383j	7.07e-42, 3.47e-103j
0.00026228330325596376424 + 1.0407971460972479648e-384j	2.23e-45, 1.1e-106j
0.25024359658693495123 + 8.3387656654427271625e-383j	1.26e-42, 6.12e-104j
3.4794606478771458294e-15 - 2.4248482867268512232e-390j	5.46e-51, 2.68e-112j
0.25024359658693495123 - 6.6901627123087645976e-383j	5.68e-43, 2.74e-104j
0.0028087610475772157675 - 3.8797686723280529899e-384j	5.25e-45, 2.56e-106j
0.017569072880805766098 - 8.6556405780374903344e-383j	1.43e-44, 6.85e-106j
0.16190629341367526765 - 8.9003875082476799384e-383j	5.43e-44, 2.52e-105j
0.00026228330325596376424 + 1.0308712433679705568e-383j	9.05e-46, 4.33e-107j
0.017569072880805766098 + 1.1021994029697487793e-383j	3e-45, 1.64e-106j
0.16190629341367526765 + 4.4881389241615653127e-383j	1.9e-44, 7.56e-106j

Download

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