Rule: Q[14]

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.

$P_{1}$ :
$\frac{5014575}{2048} \cdot t^{14} - \frac{16900975}{2048} \cdot t^{12} + \frac{22309287}{2048} \cdot t^{10} - \frac{14549535}{2048} \cdot t^{8} + \frac{4849845}{2048} \cdot t^{6} - \frac{765765}{2048} \cdot t^{4} + \frac{45045}{2048} \cdot t^{2} - \frac{429}{2048}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.98628380869681233884 + 1.2706306953299237036e-167j	2.86e-60, 2.86e-60j
-0.92843488366357351734 - 5.2011398208153035279e-170j	4.38e-60, 4.38e-60j
-0.98628380869681233884 - 7.5249747787837556576e-179j	2.46e-60, 2.46e-60j
0.10805494870734366207 - 9.6509749255538002646e-189j	9.36e-64, 9.36e-64j
0.82720131506976499319 + 5.4795233725210075994e-194j	2.74e-60, 2.74e-60j
0.68729290481168547015 + 2.2397551785179618562e-192j	6.53e-61, 6.53e-61j
-0.10805494870734366207 + 2.7826749762224545924e-198j	9.36e-64, 9.36e-64j
-0.82720131506976499319 - 1.8116373543114938753e-201j	2.64e-60, 2.64e-60j
-0.31911236892788976044 + 6.8135121736018528075e-208j	1.14e-62, 1.14e-62j
0.31911236892788976044 + 6.8894843596664498609e-215j	1.14e-62, 1.14e-62j
0.92843488366357351734 - 6.0827370636856105731e-220j	5.09e-60, 5.09e-60j
0.51524863635815409197 + 1.0790624652350371934e-225j	1.25e-61, 1.25e-61j
-0.51524863635815409197 + 4.326803039084256717e-226j	1.69e-61, 1.69e-61j
-0.68729290481168547015 + 9.5225943409724018829e-228j	8.4e-61, 8.4e-61j

Weights

Weight (ball center)	Error (ball radius)
0.035119460331751863032 - 1.6155167257341351465e-167j	3.17e-17, 1.26e-46j
0.080158087159760209806 - 8.205079630328086819e-169j	1.38e-17, 5.48e-47j
0.035119460331751863032 + 2.050271486427344499e-169j	1.07e-17, 4.26e-47j
0.2152638534631577902 - 7.5943971792366218633e-168j	4.06e-18, 1.62e-47j
0.12151857068790318469 - 1.776749932649755599e-167j	1.09e-18, 4.35e-48j
0.15720316715819353457 + 1.3903155561992842521e-167j	1.05e-18, 4.19e-48j
0.2152638534631577902 + 6.1027866752127890715e-168j	6.37e-19, 2.53e-48j
0.12151857068790318469 + 1.6349092983315159628e-168j	9.77e-20, 3.89e-49j
0.20519846372129560397 - 4.7723046736436881497e-168j	1.42e-19, 5.65e-49j
0.20519846372129560397 + 9.2965488354498100161e-168j	1.04e-19, 4.15e-49j
0.080158087159760209806 + 2.6231587554663195195e-167j	2.09e-20, 8.33e-50j
0.18553839747793781374 - 1.1316445619543188979e-167j	4.84e-20, 1.93e-49j
0.18553839747793781374 + 3.5822381512341768852e-168j	4.75e-21, 1.94e-50j
0.15720316715819353457 - 2.5299312062318489736e-168j	3.81e-21, 1.47e-50j

Download

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