OFFSET
0,2
COMMENTS
This combination of elliptic functions appears in the expression for the vector potential generated by a circular loop of current. The denominators are powers of 2. The base-2 logarithm of the denominators increments in pattern related to A090739. That latter sequence begins 3,4,3,5,3,4,3,6. Add 2 to each entry; thus, 5,6,5,7,5,6,5,8. Duplicate each entry; thus, 5,5,6,6,5,5,7,7,5,5,6,6,5,5,8,8. Now insert a 2 at the beginning and between each entry; thus, 2,5,2,5,2,6,2,6,2,5,2,5,2, 7,2,7,2,5,2,5,2,6,2,6,2,5,2,5,2,8,2,8. Finally, prepend a 4; thus 4,2,5,2,5,2,6,2,6,2,5,2,5,2,7,2,7,2,5,2,5,2,6,2,6,2,5,2,5,2,8,2,8. This yields the pattern of increments in the base-2 logarithm of the denominators. See also the construction of the ruler sequence A007814.
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 denominator of the fraction ((2n-1)!!)^2/(2^(2n+1)*(n-1)!*(n+1)!).
MATHEMATICA
Denominator[CoefficientList[Series[((2-m)EllipticK[m]-2EllipticE[m])/m, {m, 0, 20}]/Pi, m]]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Dan T. Abell, Apr 28 2011
STATUS
approved