Rule: Q[10]

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.

$P_{1}$ :
$512 \cdot t^{10} - 1280 \cdot t^{8} + 1120 \cdot t^{6} - 400 \cdot t^{4} + 50 \cdot t^{2} - 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.98768834059513772619 - 1.4561893716136811991e-183j	1.15e-61, 1.15e-61j
-0.98768834059513772619 - 2.2839144381961737557e-186j	1.06e-61, 1.06e-61j
-0.89100652418836786236 + 1.2203994455278788125e-189j	1.67e-61, 1.67e-61j
0.45399049973954679156 + 1.8812450543475749357e-198j	8.93e-63, 8.93e-63j
0.89100652418836786236 - 3.4810026238314694034e-214j	1.62e-61, 1.62e-61j
0.7071067811865475244 + 1.1481857820789442215e-224j	6.85e-62, 6.85e-62j
0.15643446504023086901 + 2.638294536026985803e-228j	6.41e-64, 6.41e-64j
-0.7071067811865475244 - 4.3477754194780649831e-230j	6.85e-62, 6.85e-62j
-0.45399049973954679156 - 6.0543024323605867277e-234j	9.6e-63, 9.6e-63j
-0.15643446504023086901 + 4.349120760297329769e-240j	6.41e-64, 6.41e-64j

Weights

Weight (ball center)	Error (ball radius)
0.1 + 2.9387320929747281969e-183j	2.3e-22, 2.66e-52j
0.1 - 7.8325593396438806384e-185j	9.12e-23, 1.06e-52j
0.1 + 2.3180071161255281617e-184j	8.42e-23, 9.75e-53j
0.1 - 1.5549734874636135529e-183j	2.53e-23, 2.92e-53j
0.1 - 4.3714190292877379304e-183j	1.39e-23, 1.61e-53j
0.1 + 2.3465189676448475394e-183j	1.14e-23, 1.32e-53j
0.1 + 1.1073027171683630327e-183j	2.35e-24, 2.72e-54j
0.1 - 3.9205714235883903166e-184j	6.16e-25, 7.16e-55j
0.1 + 5.777424874769714287e-184j	3.46e-25, 4.02e-55j
0.1 - 8.0532172437083369256e-184j	3.45e-25, 3.96e-55j

Download

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