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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 (list; graph; refs; listen; history; text; internal format)
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 ((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
KEYWORD
nonn,frac
AUTHOR
Dan T. Abell, Apr 27 2011
STATUS
approved

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Last modified June 18 07:11 EDT 2024. Contains 373469 sequences. (Running on oeis4.)