Rule: Q[13]

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.

$P_{1}$ :
$4096 \cdot t^{13} - 13312 \cdot t^{11} + 16640 \cdot t^{9} - 9984 \cdot t^{7} + 2912 \cdot t^{5} - 364 \cdot t^{3} + 13 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.9927088740980539928 + 6.152091970518150259e-212j	1.54e-60, 1.54e-60j
-0.9927088740980539928 - 5.3050479987191593708e-212j	1.39e-60, 1.39e-60j
-0.93501624268541482344 + 1.3484352611847163379e-216j	2.53e-60, 2.53e-60j
-0.23931566428755776715 - 8.3436202315296425189e-219j	2.48e-63, 2.48e-63j
0.66312265824079520238 - 4.4263237302544522647e-221j	3.69e-61, 3.69e-61j
0.93501624268541482344 - 2.6214094509964130939e-224j	2.23e-60, 2.23e-60j
1.0370249519051384626e-229 - 1.4202733036961678945e-229j	2.29e-228, 2.29e-228j
-0.82298386589365639458 - 4.6534783786601164272e-231j	1.57e-60, 1.57e-60j
-0.66312265824079520238 - 3.9805072810162948453e-235j	4.03e-61, 4.03e-61j
0.23931566428755776715 + 2.6319679083868323257e-239j	2.48e-63, 2.48e-63j
0.82298386589365639458 + 8.6115402985413183734e-241j	1.51e-60, 1.51e-60j
0.46472317204376854566 - 9.6003674156898715822e-246j	3.66e-62, 3.66e-62j
-0.46472317204376854566 + 1.8785635146215778163e-248j	4.36e-62, 4.36e-62j

Weights

Weight (ball center)	Error (ball radius)
0.076923076923076923077 - 1.6372670463043864219e-211j	3.98e-20, 2.02e-49j
0.076923076923076923077 - 1.417947207415106334e-211j	1.74e-20, 8.84e-50j
0.076923076923076923077 + 2.1531237625211779835e-211j	1.42e-20, 7.23e-50j
0.076923076923076923077 + 7.4572698958882723818e-212j	2.56e-21, 1.3e-50j
0.076923076923076923077 + 1.044682040174959275e-211j	1.43e-21, 7.29e-51j
0.076923076923076923077 + 2.4754289792094275597e-211j	1.47e-21, 7.46e-51j
0.076923076923076923077 - 7.3653529718372540354e-212j	1.31e-21, 6.62e-51j
0.076923076923076923077 - 1.2559754204408934063e-211j	7.14e-22, 3.62e-51j
0.076923076923076923077 + 9.4636008632110151676e-212j	3.98e-22, 2.03e-51j
0.076923076923076923077 + 7.7278960363062108853e-212j	1.21e-22, 6.26e-52j
0.076923076923076923077 - 1.419973037519220536e-211j	3.79e-23, 1.95e-52j
0.076923076923076923077 - 8.6411129530761865739e-212j	4e-23, 2.06e-52j
0.076923076923076923077 - 8.0630215727516390249e-212j	3.2e-23, 1.41e-52j

Download

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