A273818 Decimal expansion the Bessel moment c(3,2) = Integral_{0..inf} x^2 K_0(x)^3 dx, where K_0 is the modified Bessel function of the second kind.

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

Offset

0,2

Links

Table of n, a(n) for n=0..102.

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, 2) = Gamma(1/3)^6/(96 Pi 2^(2/3)) - 4 Pi^5 2^(2/3)/(9 Gamma(1/3)^6).

Equals sqrt(3) Pi^3/288 3F2(1/2, 1/2, 1/2; 2, 2; 1/4), where 3F2 is the generalized hypergeometric function.

Example

0.188005128918534491477960566306366792062371900057305840128102...

Mathematica

c[3, 2] = Gamma[1/3]^6/(96 Pi 2^(2/3)) - 4 Pi^5 2^(2/3)/(9 Gamma[1/3]^6);
RealDigits[c[3, 2], 10, 103][[1]]

Crossrefs

Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273819 (c(3,3)).

Sequence in context: A197623 A291692 A127583 * A326801 A326802 A179639

Adjacent sequences: A273815 A273816 A273817 * A273819 A273820 A273821

Keyword

nonn,cons

Author

Jean-François Alcover, May 31 2016

Status

approved