Rule: Q[7]

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.

$P_{1}$ :
$\frac{- 1}{5040} \cdot t^{7} + \frac{7}{720} \cdot t^{6} - \frac{7}{40} \cdot t^{5} + \frac{35}{24} \cdot t^{4} - \frac{35}{6} \cdot t^{3} + \frac{21}{2} \cdot t^{2} - 7 \cdot t + 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
19.395727862262540312 - 1.0058657750832483664e-375j	4.46e-124, 4.46e-124j
4.9003530845264845681 - 4.2785876355755695753e-386j	3.12e-124, 3.12e-124j
12.734180291797813758 - 9.0880154881172804455e-396j	9.28e-124, 9.28e-124j
2.5678767449507462069 + 1.1328569792013377507e-403j	5.89e-125, 5.89e-125j
1.0266648953391919503 + 1.58824913530015901e-423j	4.95e-126, 4.95e-126j
0.19304367656036241384 - 3.5673065051502972484e-455j	1.44e-127, 1.44e-127j
8.1821534445628607911 - 5.1477597052201234747e-487j	8.22e-124, 8.22e-124j

Weights

Weight (ball center)	Error (ball radius)
3.1703154789955805623e-08 + 1.5122493809181033969e-383j	8.27e-31, 2.55e-124j
0.020633514468716939866 - 8.9209047323086157405e-382j	6.99e-28, 2.16e-121j
1.5865464348564201269e-05 - 8.6771082116525909242e-383j	5.4e-30, 1.67e-123j
0.1471263486575052784 + 1.4853940216517799374e-381j	6.92e-28, 2.15e-121j
0.42183127786171977993 - 1.4569170742785269186e-381j	1.28e-27, 3.87e-121j
0.40931895170127390213 + 5.9529863578941890119e-382j	7.51e-28, 2.23e-121j
0.0010740101432807455221 + 3.399634783755345293e-382j	3.71e-29, 1.14e-122j

Download

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