Rule: Q[15]

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.

$P_{1}$ :
$\frac{9694845}{2048} \cdot t^{15} - \frac{35102025}{2048} \cdot t^{13} + \frac{50702925}{2048} \cdot t^{11} - \frac{37182145}{2048} \cdot t^{9} + \frac{14549535}{2048} \cdot t^{7} - \frac{2909907}{2048} \cdot t^{5} + \frac{255255}{2048} \cdot t^{3} - \frac{6435}{2048} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.98799251802048542849 - 1.3970404482129387256e-152j	5.44e-60, 5.44e-60j
-0.57097217260853884754 - 7.1542842669602742258e-168j	4.12e-61, 4.12e-61j
-0.93727339240070590431 - 1.5251741676448144604e-164j	1.1e-59, 1.1e-59j
0.57097217260853884754 - 1.0503973155449348398e-163j	4.28e-61, 4.28e-61j
0.93727339240070590431 - 7.0948040828628908426e-176j	9.1e-60, 9.1e-60j
0.72441773136017004742 + 8.0127187897631599313e-183j	2.5e-60, 2.5e-60j
-0.2011940939974345223 - 3.8356663607647053196e-192j	3.05e-63, 3.05e-63j
-0.8482065834104272162 - 3.0432834449111874526e-188j	6.35e-60, 6.35e-60j
-0.3941513470775633699 + 1.7383787899322896609e-191j	3.9e-62, 3.9e-62j
0.3941513470775633699 - 2.1181645548817206976e-188j	3.88e-62, 3.88e-62j
0.8482065834104272162 - 7.8711815641973187414e-199j	7.04e-60, 7.04e-60j
0.2011940939974345223 - 8.8818997977309866955e-207j	3.05e-63, 3.05e-63j
-0.98799251802048542849 + 1.0899195586015938163e-208j	5.06e-60, 5.06e-60j
-0.72441773136017004742 - 9.2915850302675936374e-209j	2.26e-60, 2.26e-60j
-1.2338084265255587255e-208 + 7.8705190844619616694e-209j	2.2e-207, 2.2e-207j

Weights

Weight (ball center)	Error (ball radius)
0.030753241996117268355 + 1.7782255772410257173e-152j	4.53e-19, 1.32e-47j
0.16626920581699393355 + 3.4050045621894016628e-153j	1.67e-19, 4.88e-48j
0.070366047488108124709 - 7.6161116696540639927e-154j	1e-19, 2.92e-48j
0.16626920581699393355 + 1.2729071716170554165e-152j	7.34e-20, 2.14e-48j
0.070366047488108124709 - 2.8910277904318445756e-152j	3.88e-20, 1.13e-48j
0.13957067792615431445 - 1.5493915902033396514e-152j	5.34e-20, 1.56e-48j
0.19843148532711157646 + 5.8184002968141331102e-153j	6.22e-21, 1.81e-49j
0.10715922046717193501 + 1.4973309979818662603e-153j	1.17e-21, 3.39e-50j
0.18616100001556221103 - 4.5493486837359161968e-153j	5.91e-21, 1.72e-49j
0.18616100001556221103 - 1.0588444656781888265e-152j	2.59e-21, 7.56e-50j
0.10715922046717193501 + 1.9668630042435798898e-152j	2.15e-21, 6.26e-50j
0.19843148532711157646 + 8.7940742191146634505e-153j	9.67e-22, 2.81e-50j
0.030753241996117268355 + 2.1742838228821451731e-154j	3.07e-23, 8.81e-52j
0.13957067792615431445 - 2.3848289742208532284e-153j	2.54e-22, 7.17e-51j
0.20257824192556127288 - 7.2237687013489828779e-153j	3.06e-22, 9.19e-51j

Download

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