Rule: Q[1, 2, 4]

Type

This rule is of Legendre 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.

$P_{1}$ :
$t$
$P_{2}$ :
$t^{3} - \frac{3}{5} \cdot t$
$P_{3}$ :
$t^{7} - \frac{77}{45} \cdot t^{5} + \frac{749}{891} \cdot t^{3} - \frac{31}{297} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.96049126870802028342 + 8.8253901309920072671e-185j	1.73e-62, 1.73e-62j
-0.77459666924148337704 + 3.1562054625721003772e-191j	2.04e-62, 2.04e-62j
-0.96049126870802028342 + 2.5516019074809772891e-203j	1.56e-62, 1.56e-62j
-0.434243749346802558 - 5.9409111446723744485e-212j	3.55e-63, 3.55e-63j
0.434243749346802558 - 1.8130221999122236476e-217j	4.31e-63, 4.31e-63j
0.77459666924148337704 - 5.7861103597786887564e-237j	1.97e-62, 1.97e-62j
1.4860136122877276258e-357 + 4.9142065197732035127e-237j	3.44e-236, 3.44e-236j

Weights

Weight (ball center)	Error (ball radius)
0.10465622602646726519 - 9.3606980610311690306e-185j	6.14e-27, 1.92e-57j
0.26848808986833344073 + 1.4601471456997978817e-185j	2.69e-27, 8.43e-58j
0.10465622602646726519 - 4.808106340645780858e-186j	1.41e-27, 4.41e-58j
0.40139741477596222291 - 2.5399044210651496146e-185j	9.67e-28, 3.07e-58j
0.40139741477596222291 - 6.7316028455469478564e-185j	4.59e-28, 1.41e-58j
0.26848808986833344073 + 1.3628596460354277451e-184j	3.11e-28, 9.22e-59j
0.45091653865847414235 + 4.024272355653769255e-185j	3.06e-28, 9.9e-59j

Download

All rules of Legendre type can be downloaded here packed into a single file.