Rule: Q[8]

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.

$P_{1}$ :
$\frac{1}{40320} \cdot t^{8} - \frac{1}{630} \cdot t^{7} + \frac{7}{180} \cdot t^{6} - \frac{7}{15} \cdot t^{5} + \frac{35}{12} \cdot t^{4} - \frac{28}{3} \cdot t^{3} + 14 \cdot t^{2} - 8 \cdot t + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
15.740678641278004578 - 5.1935504725044763767e-127j	1.92e-59, 1.92e-59j
22.863131736889264106 + 6.6215514379261715957e-131j	7.65e-60, 7.65e-60j
7.0459054023934656973 + 2.5259214164452253707e-136j	1.03e-59, 1.03e-59j
10.758516010180995224 - 3.5036454165704266178e-145j	1.84e-59, 1.84e-59j
2.2510866298661306893 + 2.3671491578516281168e-157j	4.59e-61, 4.59e-61j
0.90370177679937991219 - 2.5111904816421835553e-174j	2.89e-62, 2.89e-62j
4.2667001702876587936 - 4.7436471954082039061e-184j	2.86e-60, 2.86e-60j
0.17027963230510099979 - 8.5287685388614979083e-189j	1.44e-63, 1.44e-63j

Weights

Weight (ball center)	Error (ball radius)
8.4857467162725315449e-07 + 2.0635687385829621856e-133j	8.65e-28, 3.07e-57j
1.0480011748715103816e-09 + 2.6206637555081692883e-135j	4.28e-29, 1.52e-58j
0.0027945362352256725249 + 1.9460925912342769136e-132j	1.6e-26, 5.68e-56j
9.0765087733582131042e-05 - 7.5633822972941381272e-133j	3.15e-27, 1.12e-56j
0.1757949866371718057 + 5.6234029019892663655e-132j	9.26e-26, 3.29e-55j
0.41878678081434295608 - 4.9999117696845392627e-132j	1.88e-25, 6.25e-55j
0.033343492261215651522 - 3.9640229304331417313e-132j	3.06e-26, 1.09e-55j
0.36918858934163752992 + 1.9417998990097471397e-132j	1.2e-25, 3.82e-55j

Download

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