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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
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 01 2016

STATUS

approved

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Last modified May 8 18:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)