Rule: Q[11]

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.

$P_{1}$ :
$2048 \cdot t^{11} - 56320 \cdot t^{9} + 506880 \cdot t^{7} - 1774080 \cdot t^{5} + 2217600 \cdot t^{3} - 665280 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.7832900997816517708 - 3.1698916458157204447e-132j	2.18e-61, 2.18e-61j
3.6684708465595825185 + 3.0818391000986170991e-133j	6.46e-62, 6.46e-62j
2.0259480158257553352 - 3.6982069201183405189e-132j	1.32e-61, 1.32e-61j
-2.0259480158257553352 + 1.6794690268917721879e-139j	1.34e-61, 1.34e-61j
-0.65680956688209976502 + 2.8029163332563412942e-145j	6.67e-63, 6.67e-63j
-3.6684708465595825185 - 1.4916681462400413487e-153j	6.46e-62, 6.46e-62j
-2.7832900997816517708 + 1.8548144395822933178e-168j	2.03e-61, 2.03e-61j
-4.2414589625810760472e-179 + 3.0846974273316916707e-178j	3.43e-177, 3.43e-177j
-1.3265570844949328559 + 3.2175901519241693161e-186j	3.55e-62, 3.55e-62j
0.65680956688209976502 - 4.3836186980168060795e-192j	6.67e-63, 6.67e-63j
1.3265570844949328559 - 2.4657855176344534197e-193j	2.85e-62, 2.85e-62j

Weights

Weight (ball center)	Error (ball radius)
0.00019567193027122338993 + 7.3303521879011505668e-135j	2.72e-25, 6.64e-56j
8.1218497902149142258e-07 - 1.2211548678189746019e-136j	1.3e-26, 3.18e-57j
0.0067202852355372787064 + 4.553737569276286884e-134j	1.22e-24, 2.97e-55j
0.0067202852355372787064 + 5.3738432398477245346e-135j	1.23e-25, 3e-56j
0.24224029987396995101 + 4.9243902057262324424e-134j	1.47e-24, 3.57e-55j
8.1218497902149142258e-07 + 4.1752385533085924978e-137j	3.12e-28, 7.62e-59j
0.00019567193027122338993 - 7.6977808895362718822e-136j	4.82e-27, 1.18e-57j
0.36940836940836940837 - 8.1222685135562042678e-134j	5.23e-25, 1.27e-55j
0.066138746071057821217 - 2.0467496654016826937e-134j	1.48e-25, 3.62e-56j
0.24224029987396995101 + 9.8675239498425952539e-134j	1.43e-25, 3.51e-56j
0.066138746071057821217 - 1.0362038969641871257e-133j	6.68e-26, 1.56e-56j

Download

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