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

0,3

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

Formula

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

Mathematica

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

Crossrefs

Cf. A189806.

Sequence in context: A290774 A229852 A265956 * A230145 A343808 A125520

Adjacent sequences: A189802 A189803 A189804 * A189806 A189807 A189808

Keyword

nonn,frac

Author

Dan T. Abell, Apr 27 2011

Status

approved