Rule: Q[5]

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.

$P_{1}$ :
$\frac{63}{8} \cdot t^{5} - \frac{35}{4} \cdot t^{3} + \frac{15}{8} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.53846931010568309104 - 2.3656081334167690636e-78j	1.44e-63, 1.44e-63j
-0.53846931010568309104 - 1.5133754590909123358e-83j	1.78e-63, 1.78e-63j
-0.9061798459386639928 + 2.0788133335218740215e-93j	3.02e-63, 3.02e-63j
-5.1977048828224496093e-113 - 5.1977048828224496093e-113j	3.68e-112, 3.68e-112j
0.9061798459386639928 + 2.8853058180580424315e-129j	2.22e-63, 2.22e-63j

Weights

Weight (ball center)	Error (ball radius)
0.47862867049936646804 + 8.58637093296843641e-79j	7.9e-30, 4.97e-61j
0.47862867049936646804 + 1.0513523601501313549e-78j	3.44e-30, 2.13e-61j
0.23692688505618908751 - 2.7674714903049639465e-79j	1.48e-30, 8.53e-62j
0.56888888888888888889 - 2.7204919178361368262e-78j	1.93e-30, 1.52e-61j
0.23692688505618908751 + 1.0872496134196582249e-78j	9.89e-31, 4.7e-62j

Download

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