Rule: Q[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.

$P_{1}$ :
$\frac{35}{8} \cdot t^{4} - \frac{15}{4} \cdot t^{2} + \frac{3}{8}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.86113631159405257522 + 7.6996933697913992575e-69j	1.67e-63, 1.67e-63j
-0.3399810435848562648 - 6.8205577887142092753e-81j	9.26e-64, 9.26e-64j
-0.86113631159405257522 + 6.4444240436655155101e-99j	1.02e-63, 1.02e-63j
0.3399810435848562648 + 2.9741505906042764335e-118j	9.26e-64, 9.26e-64j

Weights

Weight (ball center)	Error (ball radius)
0.34785484513745385737 - 8.9243482813642088056e-69j	9.07e-30, 2.71e-61j
0.65214515486254614263 - 5.6481112822997464205e-69j	4.18e-30, 1.28e-61j
0.34785484513745385737 + 1.5551403469393324536e-69j	1.88e-30, 5.93e-62j
0.65214515486254614263 + 1.3017319216724622773e-68j	3.01e-30, 8.38e-62j

Download

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