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A273986
Decimal expansion of the odd Bessel moment s(5,5) (see the referenced paper about the elliptic integral evaluations of Bessel moments).
5
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
OFFSET
0,2
LINKS
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
s[5, 5] = NIntegrate[x^5*BesselI[0, x]*BesselK[0, x]^4, {x, 0, Infinity}, WorkingPrecision -> 103];
Join[{0}, RealDigits[s[5, 5]][[1]]]
CROSSREFS
Cf. A073010 (s(3,1)), A121839 (1+s(3,3)), A222068 (s(4,1)), A244854 (2s(4,3)), A273959, A273984 (s(5,1)), A273985 (s(5,3)).
Sequence in context: A019117 A204372 A279918 * A246729 A337029 A293557
KEYWORD
nonn,cons
AUTHOR
STATUS
approved