Rule: Q[2, 7]

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.

$P_{1}$ :
$\frac{3}{2} \cdot t^{2} - \frac{1}{2}$
$P_{2}$ :
$\frac{3}{2} \cdot t^{9} - \frac{151}{50} \cdot t^{7} + \frac{1281}{650} \cdot t^{5} - \frac{651}{1430} \cdot t^{3} + \frac{56}{2145} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.96392874096524810675 - 4.7068747365290705425e-184j	4.5e-62, 4.5e-62j
-0.57735026918962576451 + 3.1601331849255234355e-187j	2.34e-62, 2.34e-62j
-0.96392874096524810675 + 8.6970994968653432617e-190j	4.5e-62, 4.5e-62j
0.29036229308829455553 - 1.0033306956520399657e-197j	3.78e-63, 3.78e-63j
0.81641357233552832956 - 1.9010915662951598235e-210j	7.75e-62, 7.75e-62j
0.57735026918962576451 - 4.4263237302544522647e-221j	2.34e-62, 2.34e-62j
0 + 0j	0, 0j
-0.81641357233552832956 + 2.5160737381238801985e-233j	7.75e-62, 7.75e-62j
-0.29036229308829455553 + 0j	3.78e-63, 3.78e-63j

Weights

Weight (ball center)	Error (ball radius)
0.09183134281931075609 + 6.2304887395731024535e-184j	1.7e-24, 4.56e-55j
0.27158424140821458508 + 2.0919934833686017307e-184j	6.72e-25, 1.8e-55j
0.09183134281931075609 + 2.2392040450831816998e-185j	3.31e-25, 8.89e-56j
0.29380794845818344106 - 7.6343937053369907837e-184j	3.33e-25, 8.92e-56j
0.19910299792653611573 - 1.0599282198218723928e-183j	1.48e-25, 3.97e-56j
0.27158424140821458508 + 8.3351460879659817106e-184j	1.26e-25, 3.4e-56j
0.28734693877551020408 + 6.3322903758858563398e-184j	5.32e-26, 1.42e-56j
0.19910299792653611573 - 8.7648527473075194617e-185j	6.01e-27, 1.8e-57j
0.29380794845818344106 - 4.1036779130153937467e-184j	3.2e-26, 8.25e-57j

Download

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