A273839 Decimal expansion the Bessel moment c(4,0) = Integral_{0..inf} K_0(x)^4 dx, where K_0 is the modified Bessel function of the second kind.

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

Offset

2,1

Links

Table of n, a(n) for n=2..103.

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

Formula

c(4,0) = (Pi^4/4) Sum_{n>=0} binomial(2n, n)^4/2^(8n).

Equals (Pi^4/4) 4F3(1/2, 1/2, 1/2, 1/2; 1, 1, 1; 1), where 4F3 is the generalized hypergeometric function.

Example

27.2413384178059734067099802645579350239978880986182746551229...

Mathematica

c[4, 0] = (Pi^4/4)*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {1, 1, 1}, 1];
RealDigits[c[4, 0], 10, 102][[1]]

Crossrefs

Cf. A273816 (c(3,0)), A273817 (c(3,1)), A273818 (c(3,2)), A273819 (c(3,3)), A233091 (c(4,1)), A273840 (c(4,2)), A273841 (c(4,3)).

Sequence in context: A196802 A196590 A197047 * A074473 A021371 A332501

Adjacent sequences: A273836 A273837 A273838 * A273840 A273841 A273842

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 01 2016

Status

approved