Rule: Q[17]

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.

$P_{1}$ :
$65536 \cdot t^{17} - 278528 \cdot t^{15} + 487424 \cdot t^{13} - 452608 \cdot t^{11} + 239360 \cdot t^{9} - 71808 \cdot t^{7} + 11424 \cdot t^{5} - 816 \cdot t^{3} + 17 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.99573417629503452187 + 2.9790023256964455348e-448j	6.93e-123, 6.93e-123j
-0.96182564317281907041 - 1.0119717148518492813e-456j	1.38e-122, 1.38e-122j
-0.89516329135506232207 - 4.8695183312264992349e-464j	7.13e-123, 7.13e-123j
-0.99573417629503452187 - 7.7518713220988341607e-473j	5.51e-123, 5.51e-123j
0.96182564317281907041 - 2.914821331556883944e-479j	1.44e-122, 1.44e-122j
0.89516329135506232207 - 9.196218130883920237e-491j	8.61e-123, 8.61e-123j
-0.18374951781657033157 - 2.0629446408862503686e-498j	4.84e-127, 4.84e-127j
-0.79801722728023950333 + 3.3227795684440296274e-497j	4.01e-123, 4.01e-123j
-0.36124166618715294874 - 1.3849741004767878417e-500j	1.03e-125, 1.03e-125j
0.36124166618715294874 + 2.5664884568945372494e-498j	1.08e-125, 1.08e-125j
0.79801722728023950333 - 1.2295979139088554945e-498j	3.48e-123, 3.48e-123j
0.18374951781657033157 + 1.7404952282187538623e-505j	6.17e-127, 6.17e-127j
-0.52643216287735580024 - 1.122753865465071385e-503j	8.93e-125, 8.93e-125j
-0.67369564364655721171 - 2.0946987247673219761e-504j	6.19e-124, 6.19e-124j
-5.9926041015947765582e-508 - 2.3124468503832804284e-507j	4.06e-506, 4.06e-506j
0.67369564364655721171 - 1.1305588419790878429e-504j	7.95e-124, 7.95e-124j
0.52643216287735580024 - 2.9779686793414766962e-516j	8.93e-125, 8.93e-125j

Weights

Weight (ball center)	Error (ball radius)
0.058823529411764705882 - 1.0247778763432416523e-447j	7.02e-48, 3.56e-107j
0.058823529411764705882 + 2.6550343324885392642e-449j	3.15e-48, 1.6e-107j
0.058823529411764705882 - 4.4769385607070078709e-449j	2.05e-48, 1.04e-107j
0.058823529411764705882 - 8.7993084340447472215e-450j	1.03e-48, 5.2e-108j
0.058823529411764705882 + 1.5327671605782232783e-447j	4.41e-49, 2.24e-108j
0.058823529411764705882 - 8.4173785154796080417e-448j	2.02e-49, 1.02e-108j
0.058823529411764705882 + 1.5827736549797382681e-448j	4.26e-50, 2.16e-109j
0.058823529411764705882 + 6.3805916578482343256e-449j	5.44e-50, 2.76e-109j
0.058823529411764705882 - 1.3050673097841677834e-448j	3.65e-50, 1.85e-109j
0.058823529411764705882 - 2.7911201276424567487e-448j	3.33e-51, 1.69e-110j
0.058823529411764705882 + 5.7886769146535143977e-448j	2.83e-51, 1.44e-110j
0.058823529411764705882 + 2.2991268366350088091e-448j	3.21e-51, 1.63e-110j
0.058823529411764705882 + 1.0608081804504777136e-448j	3.1e-51, 1.57e-110j
0.058823529411764705882 - 8.4071855228439693957e-449j	2.21e-51, 1.12e-110j
0.058823529411764705882 - 1.9073294210270632794e-448j	1.8e-51, 9.13e-111j
0.058823529411764705882 - 4.3582381860220387524e-448j	1.61e-52, 8.28e-112j
0.058823529411764705882 + 3.4406980245486469962e-448j	1.91e-52, 9.5e-112j

Download

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