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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
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 (list; constant; graph; refs; listen; history; text; internal format)
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 * A021063 A216638 A110649

Adjacent sequences:  A273813 A273814 A273815 * A273817 A273818 A273819

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 31 2016

STATUS

approved

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Last modified June 26 00:40 EDT 2019. Contains 324367 sequences. (Running on oeis4.)