Rule: Q[8]

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.

$P_{1}$ :
$128 \cdot t^{8} - 256 \cdot t^{6} + 160 \cdot t^{4} - 32 \cdot t^{2} + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.98078528040323044913 + 8.0614513290805065021e-138j	2.86e-62, 2.86e-62j
-0.98078528040323044913 - 5.0384070806753165638e-138j	2.68e-62, 2.68e-62j
-0.83146961230254523708 + 5.8941326322190491215e-143j	3.67e-62, 3.67e-62j
-0.19509032201612826785 - 3.1325031071040868322e-153j	1.15e-63, 1.15e-63j
0.55557023301960222474 + 2.4841264815834285506e-170j	6.42e-63, 6.42e-63j
0.83146961230254523708 + 5.2952340785952043603e-184j	2.98e-62, 2.98e-62j
0.19509032201612826785 - 1.4027579833653779454e-191j	6.75e-64, 6.75e-64j
-0.55557023301960222474 - 1.3912852313041620858e-195j	8.13e-63, 8.13e-63j

Weights

Weight (ball center)	Error (ball radius)
0.125 - 1.2662547238903339795e-137j	3.53e-25, 8.57e-56j
0.125 - 7.601032625390819957e-138j	1.51e-25, 3.67e-56j
0.125 + 1.0428156878576635263e-137j	1.22e-25, 2.95e-56j
0.125 - 2.7838417960640782067e-139j	4.92e-26, 1.2e-56j
0.125 - 8.3529650637382532829e-138j	1.07e-26, 2.62e-57j
0.125 + 1.8228904603706295916e-137j	7.55e-27, 1.84e-57j
0.125 + 3.7550758260018532257e-138j	7.64e-27, 1.88e-57j
0.125 - 3.5172082006459635496e-138j	4.63e-27, 1.03e-57j

Download

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