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A189805 Numerators of coefficients in the series expansion of ((2 - m) EllipticK(m) - 2 EllipticE(m))/(Pi * m). 2

%I #11 Jan 17 2018 03:33:30

%S 0,1,3,75,245,6615,22869,1288287,4601025,265939245,969738055,

%T 28510298817,105468168351,3138933581875,11734782467625,

%U 1409850293610375,5313200518272825,642897262711011825,2438232652696561875,74176455589813182375,282762879579212657625

%N Numerators of coefficients in the series expansion of ((2 - m) EllipticK(m) - 2 EllipticE(m))/(Pi * m).

%C This combination of elliptic functions appears in the expression for the vector potential generated by a circular loop of current.

%D J. D. Jackson, Classical Electrodynamics, John Wiley & Sons, third edition, 1999, eq.(5.37).

%H G. C. Greubel, <a href="/A189805/b189805.txt">Table of n, a(n) for n = 0..830</a>

%F a(n) is the numerator of the fraction ((2n-1)!!)^2/(2^(2n+1)*(n-1)!*(n+1)!).

%t Numerator[CoefficientList[Series[((2-m)EllipticK[m]-2EllipticE[m])/m,{m,0,20}]/Pi,m]]

%Y Cf. A189806.

%K nonn,frac

%O 0,3

%A _Dan T. Abell_, Apr 27 2011

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