Rule: Q[3, 4]

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.

$P_{1}$ :
$4 \cdot t^{3} - 3 \cdot t$
$P_{2}$ :
$4 \cdot t^{7} - 8 \cdot t^{5} + \frac{19}{4} \cdot t^{3} - \frac{3}{4} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
1 - 7.3476769926515033223e-140j	2.13e-62, 2.13e-62j
-0.86602540378443864676 - 2.7968777742000775287e-155j	2.56e-62, 2.56e-62j
-1 + 5.6857142980577740874e-175j	2.13e-62, 2.13e-62j
-0.5 - 9.7676843897697997097e-187j	2.53e-63, 2.53e-63j
0.5 - 1.5710889413692232989e-189j	2.53e-63, 2.53e-63j
0.86602540378443864676 + 5.7863766813821840249e-191j	2.56e-62, 2.56e-62j
-3.2106582260865278903e-196 + 1.0702194086955092968e-195j	7.82e-195, 7.82e-195j

Weights

Weight (ball center)	Error (ball radius)
0.083333333333333333333 + 7.4497280619938854378e-140j	2.99e-27, 1.28e-57j
0.16666666666666666667 - 6.5626803880856940733e-141j	1.32e-27, 5.66e-58j
0.083333333333333333333 + 3.0615320802714423208e-141j	8.32e-28, 3.56e-58j
0.16666666666666666667 + 8.1640855473905719823e-141j	3.8e-28, 1.66e-58j
0.16666666666666666667 + 2.4492256642171681153e-140j	1.83e-28, 7.68e-59j
0.16666666666666666667 - 9.1406346180601011508e-140j	1.67e-28, 6.78e-59j
0.16666666666666666667 - 1.2246128321085844253e-140j	1.11e-28, 4.92e-59j

Download

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