Rule: Q[12]

Type

This rule is of Chebyshev U (second kind) 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.

$P_{1}$ :
$4096 \cdot t^{12} - 11264 \cdot t^{10} + 11520 \cdot t^{8} - 5376 \cdot t^{6} + 1120 \cdot t^{4} - 84 \cdot t^{2} + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.97094181742605202716 - 7.071289082841870819e-155j	3.4e-61, 3.4e-61j
-0.97094181742605202716 - 3.3562533290400930345e-154j	3.23e-61, 3.23e-61j
-0.8854560256532098959 + 8.8910349979403099338e-162j	4.71e-61, 4.71e-61j
0.74851074817110109863 - 1.0242815282356161499e-164j	2.69e-61, 2.69e-61j
0.56806474673115580251 - 3.7308267584740985592e-166j	9.8e-62, 9.8e-62j
-0.74851074817110109863 + 2.5876317516494047402e-169j	3.35e-61, 3.35e-61j
0.35460488704253562597 + 6.4778645973965525085e-178j	1.14e-62, 1.14e-62j
0.8854560256532098959 - 3.1624314636054692707e-184j	4.68e-61, 4.68e-61j
-0.12053668025532305335 - 4.9534891287589908698e-191j	9.34e-64, 9.34e-64j
-0.35460488704253562597 - 2.5994444432462456133e-202j	1.14e-62, 1.14e-62j
-0.56806474673115580251 - 2.1577389277450063997e-209j	7.83e-62, 7.83e-62j
0.12053668025532305335 + 1.3416364279350454992e-215j	9.34e-64, 9.34e-64j

Weights

Weight (ball center)	Error (ball radius)
0.0044055374748765424654 + 8.6835195837760393521e-156j	4.09e-21, 2.22e-50j
0.0044055374748765424654 - 3.7761118143624051784e-155j	1.65e-21, 8.93e-51j
0.016612894356494007596 + 6.5856610347326250109e-155j	1.48e-21, 8.02e-51j
0.033825512297872190256 + 1.735595059931255613e-155j	4.04e-22, 2.19e-51j
0.052100187963174447153 - 2.0506581072615679691e-155j	2.84e-22, 1.54e-51j
0.033825512297872190256 - 5.2430261840308715576e-155j	1.01e-22, 5.49e-52j
0.067250413391196196101 + 2.4743348715674908667e-155j	7.28e-23, 3.94e-52j
0.016612894356494007596 - 1.6745509791814891263e-155j	7.65e-23, 4.15e-52j
0.075805454516386616429 + 3.4828934993478761429e-155j	1.03e-23, 5.61e-53j
0.067250413391196196101 - 4.0208665468307594326e-155j	4.36e-24, 2.38e-53j
0.052100187963174447153 + 4.5797026420687804873e-155j	3.29e-24, 1.79e-53j
0.075805454516386616429 - 2.961325434358538792e-155j	3.92e-24, 2.07e-53j

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.