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

0, 1, 3, 75, 245, 6615, 22869, 1288287, 4601025, 265939245, 969738055, 28510298817, 105468168351, 3138933581875, 11734782467625, 1409850293610375, 5313200518272825, 642897262711011825, 2438232652696561875, 74176455589813182375, 282762879579212657625

Offset: 0

Author

Dan T. Abell, Apr 27 2011

Keywords

• nonn
• frac

Comments

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

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..830

Crossrefs

Cf. A189806.

Programs

Mathematica

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

Formula

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