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A273840 Decimal expansion the Bessel moment c(4,2) = Integral_{0..inf} x^2 K_0(x)^4 dx, where K_0 is the modified Bessel function of the second kind. 2
1, 9, 5, 7, 7, 0, 6, 2, 5, 2, 4, 7, 2, 8, 7, 9, 1, 7, 2, 1, 7, 4, 5, 8, 0, 8, 3, 2, 7, 5, 5, 7, 7, 2, 3, 7, 4, 1, 8, 8, 2, 7, 8, 9, 6, 9, 6, 6, 5, 2, 5, 0, 2, 8, 1, 9, 7, 9, 3, 3, 8, 4, 6, 1, 6, 6, 3, 5, 2, 9, 9, 2, 9, 6, 9, 4, 4, 4, 4, 6, 2, 6, 5, 5, 3, 5, 2, 9, 1, 1, 1, 6, 3, 8, 5, 8, 0, 8, 5, 7, 6, 8, 8, 9 (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.

FORMULA

c(4,2) = (Pi^4/64)*(4 * 4F3(1/2, 1/2, 1/2, 1/2; 1, 1, 1; 1) - 3 * 4F3(1/2, 1/2, 1/2, 1/2; 2, 1, 1; 1)) - 3*Pi^2/16, where 4F3 is the generalized hypergeometric function.

EXAMPLE

0.195770625247287917217458083275577237418827896966525028197933846...

MATHEMATICA

c[4, 2] = (Pi^4/64)*(4*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {1, 1, 1}, 1] - 3*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {2, 1, 1}, 1]) - 3*Pi^2 / 16;

RealDigits[c[4, 2], 10, 104][[1]]

CROSSREFS

Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)), A273839 (c(4,0)), A233091 (c(4,1)), A273841 (c(4,3)).

Sequence in context: A021515 A011259 A155754 * A117019 A155692 A011203

Adjacent sequences:  A273837 A273838 A273839 * A273841 A273842 A273843

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 01 2016

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)