Rule: Q[6]

Type

This rule is of Laguerre 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.

$P_{1}$ :
$\frac{1}{720} \cdot t^{6} - \frac{1}{20} \cdot t^{5} + \frac{5}{8} \cdot t^{4} - \frac{10}{3} \cdot t^{3} + \frac{15}{2} \cdot t^{2} - 6 \cdot t + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
15.982873980601701783 + 4.2035924361754560425e-148j	6.96e-61, 6.96e-61j
9.8374674183825899177 + 1.1380524797363596715e-159j	1.33e-60, 1.33e-60j
5.7751435691045105018 + 9.9365059263337142025e-170j	9.01e-61, 9.01e-61j
0.22284660417926068946 - 1.084463939296297853e-180j	1.38e-63, 1.38e-63j
1.1889321016726230307 - 8.6970994968653432617e-190j	2.42e-62, 2.42e-62j
2.9927363260593140777 + 1.8943092561138775394e-199j	2.04e-61, 2.04e-61j

Weights

Weight (ball center)	Error (ball radius)
8.9854790642962123883e-07 - 1.7704028270295996794e-154j	1.09e-30, 8.05e-61j
0.00026101720281493205948 + 8.2184398670617915763e-154j	9.39e-30, 6.96e-60j
0.010399197453149074899 - 2.3928523178329705361e-153j	3.78e-29, 2.82e-59j
0.45896467394996359357 + 2.0225508772515558929e-153j	3.75e-28, 2.95e-58j
0.41700083077212099411 - 4.7438053571084435695e-153j	3.09e-28, 2.47e-58j
0.11337338207404497574 + 4.469303093686639023e-153j	9.77e-29, 7e-59j

Download

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