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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. 6
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 (list; constant; graph; refs; listen; history; text; internal format)
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 * A179639 A113809 A231097

Adjacent sequences:  A273815 A273816 A273817 * A273819 A273820 A273821

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 31 2016

STATUS

approved

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Last modified June 18 14:52 EDT 2019. Contains 324213 sequences. (Running on oeis4.)