A273986 - OEIS

A273986

Decimal expansion of the odd Bessel moment s(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).

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

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..103.

David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891, page 21.

FORMULA

s(5,5) = Integral_{0..inf} x^5*BesselI_0(x)*BesselK_0(x)^4 dx.

Equals Pi^2 (4/15)^3 (43 C - 19/(40 C)) (conjectural, where C is A273959).

EXAMPLE

0.054514253132761880363033919802009596877614349544575913649940264634...

MATHEMATICA