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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 (list; constant; graph; refs; listen; history; text; internal format)
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

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 A293557 A123587

Adjacent sequences:  A273983 A273984 A273985 * A273987 A273988 A273989

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 06 2016

STATUS

approved

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Last modified October 22 12:47 EDT 2019. Contains 328318 sequences. (Running on oeis4.)