

A189805


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


2



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



FORMULA

a(n) is the numerator of the fraction ((2n1)!!)^2/(2^(2n+1)*(n1)!*(n+1)!).


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,frac


AUTHOR



STATUS

approved



