A273816 Decimal expansion the Bessel moment c(3,0) = Integral_{0..inf} K_0(x)^3 dx, where K_0 is the modified Bessel function of the second kind.

6, 9, 4, 8, 8, 2, 2, 7, 8, 1, 0, 7, 9, 6, 2, 9, 7, 8, 9, 4, 3, 6, 4, 3, 6, 4, 4, 5, 4, 7, 0, 8, 2, 9, 7, 5, 7, 6, 7, 4, 8, 5, 1, 1, 3, 2, 6, 0, 9, 8, 9, 1, 7, 3, 5, 1, 6, 2, 3, 8, 0, 6, 8, 8, 1, 9, 1, 4, 2, 2, 3, 3, 8, 1, 9, 9, 8, 0, 4, 1, 8, 6, 8, 3, 9, 9, 5, 2, 3, 5, 1, 8, 0, 6, 0, 9, 5, 5, 3, 7, 1, 9, 3

Offset

1,1

Links

Table of n, a(n) for n=1..103.

David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891 [hep-th], 2008.

Formula

c(3, 0) = 3*Gamma(1/3)^6/(32*Pi*2^(2/3)).

Equals (1/2)*Pi*K[(1/4)*(2 - Sqrt[3])]*K[(1/4)*(2 + Sqrt[3])], where K(x) is the complete elliptic integral of the first kind.

Also equals sqrt(3) Pi^3/8 3F2(1/2, 1/2, 1/2; 1, 1; 1/4), where 3F2 is the generalized hypergeometric function A263490.

Example

6.94882278107962978943643644547082975767485113260989173516238...

Mathematica

c[3, 0] = 3*Gamma[1/3]^6/(32*Pi*2^(2/3));
RealDigits[c[3, 0], 10, 103][[1]]

Crossrefs

Cf. A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)).

Sequence in context: A246041 A131691 A258504 * A350817 A021063 A216638

Adjacent sequences: A273813 A273814 A273815 * A273817 A273818 A273819

Keyword

nonn,cons

Author

Jean-François Alcover, May 31 2016

Status

approved