Rule: Q[14]

Type

This rule is of Chebyshev T (first 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.

$P_{1}$ :
$8192 \cdot t^{14} - 28672 \cdot t^{12} + 39424 \cdot t^{10} - 26880 \cdot t^{8} + 9408 \cdot t^{6} - 1568 \cdot t^{4} + 98 \cdot t^{2} - 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.99371220989324258353 + 8.2375481105557111419e-127j	3.41e-60, 3.41e-60j
-0.99371220989324258353 + 3.4992988961407938609e-125j	3.1e-60, 3.1e-60j
-0.9438833303083675629 - 6.5370209940377523838e-128j	6.78e-60, 6.78e-60j
0.11196447610330785847 + 1.3221640067833799251e-132j	1.14e-63, 1.14e-63j
0.84672419922828416835 + 3.4458636967769661786e-139j	3.46e-60, 3.46e-60j
0.9438833303083675629 - 1.4915128252493922146e-138j	5.97e-60, 5.97e-60j
-0.11196447610330785847 + 1.1029716021335124965e-140j	9.89e-64, 9.89e-64j
-0.84672419922828416835 - 2.8817483551291758931e-144j	3.63e-60, 3.63e-60j
-0.33027906195516708177 + 3.4642978362085517094e-148j	1.39e-62, 1.39e-62j
0.53203207651533656356 + 1.6062282598712765242e-150j	2.31e-61, 2.31e-61j
0.7071067811865475244 + 5.7394262658064090954e-155j	8.46e-61, 8.46e-61j
0.33027906195516708177 + 1.3185080930516416499e-165j	1.11e-62, 1.11e-62j
-0.53203207651533656356 + 3.5763210798126800307e-178j	1.74e-61, 1.74e-61j
-0.7071067811865475244 + 5.9019796501009048599e-184j	9.7e-61, 9.7e-61j

Weights

Weight (ball center)	Error (ball radius)
0.071428571428571428571 - 3.5905362108344570595e-126j	7.79e-17, 3.79e-46j
0.071428571428571428571 + 9.9063497757171405412e-125j	3.31e-17, 1.61e-46j
0.071428571428571428571 - 1.4807943928824475425e-124j	2.91e-17, 1.41e-46j
0.071428571428571428571 - 2.066898873004281181e-125j	7.94e-18, 3.86e-47j
0.071428571428571428571 - 8.3597714405766899641e-126j	2.58e-18, 1.25e-47j
0.071428571428571428571 + 7.2910786036982690541e-126j	3.59e-18, 1.74e-47j
0.071428571428571428571 + 2.5647939951796348878e-125j	9.72e-19, 4.73e-48j
0.071428571428571428571 + 8.1032550053703219056e-125j	1.75e-19, 8.5e-49j
0.071428571428571428571 - 3.21573752906311157e-125j	2.39e-19, 1.16e-48j
0.071428571428571428571 - 1.3360824622991471677e-125j	8.47e-20, 4.12e-49j
0.071428571428571428571 + 1.0583712212765783483e-125j	8.85e-20, 4.3e-49j
0.071428571428571428571 + 1.6673118378158574541e-125j	5.7e-20, 2.77e-49j
0.071428571428571428571 + 4.1263129778160304646e-125j	4.83e-21, 2.41e-50j
0.071428571428571428571 - 5.5338091152132604615e-125j	4.17e-21, 1.96e-50j

Download

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