Rule: Q[11]

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.

$P_{1}$ :
$t^{11} - 55 \cdot t^{9} + 990 \cdot t^{7} - 6930 \cdot t^{5} + 17325 \cdot t^{3} - 10395 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
6.4491610632644052017e-137 + 5.3743008860536710014e-137j	9.23e-136, 9.23e-136j
-5.1880012243748709482 - 4.5824045452494070231e-151j	9.77e-62, 9.77e-62j
-2.8651231606436449977 - 2.9147084050578894994e-168j	1.59e-61, 1.59e-61j
-3.9361666071299769287 - 2.4677579418653533366e-178j	2.52e-61, 2.52e-61j
2.8651231606436449977 - 9.639679460411536471e-180j	1.81e-61, 1.81e-61j
5.1880012243748709482 - 1.6944749051504653953e-182j	1.37e-61, 1.37e-61j
0.92886899738106394014 + 9.1931147197833409032e-186j	8.11e-63, 8.11e-63j
-1.8760350201548458453 + 7.1821208748307350807e-189j	4.54e-62, 4.54e-62j
-0.92886899738106394014 - 6.5754280470252091193e-193j	1.02e-62, 1.02e-62j
3.9361666071299769287 + 3.9452568282151254716e-192j	2.52e-61, 2.52e-61j
1.8760350201548458453 + 1.2842632904346111561e-195j	4.27e-62, 4.27e-62j

Weights

Weight (ball center)	Error (ball radius)
0.36940836940836940837 + 4.8380928526982749459e-155j	1.7e-22, 1.64e-53j
8.1218497902149142258e-07 + 5.6741753043202756427e-141j	5.72e-25, 5.54e-56j
0.0067202852355372787064 + 9.3460026650611822585e-139j	6.67e-23, 6.45e-54j
0.00019567193027122338993 - 1.1608233478711452617e-139j	6.14e-24, 5.95e-55j
0.0067202852355372787064 - 9.3460026650611824463e-139j	1.01e-24, 9.76e-56j
8.1218497902149142258e-07 - 5.674175304320276644e-141j	2.87e-27, 2.78e-58j
0.24224029987396995101 - 1.7307887852911210944e-137j	5.1e-23, 4.95e-54j
0.066138746071057821217 - 4.4777761605744279906e-138j	8.2e-24, 7.96e-55j
0.24224029987396995101 + 1.7307887852911210863e-137j	3.49e-23, 3.39e-54j
0.00019567193027122338993 + 1.1608233478711453141e-139j	3.54e-26, 3.43e-57j
0.066138746071057821217 + 4.4777761605744280377e-138j	1.15e-24, 1.09e-55j

Download

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