A190573 Decimal expansion of Integral_{x = 0 to oo} Product_{m=1..oo} cos(x/m) dx.

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

Offset

0,1

References

J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 101.

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.3, p. 429.

Links

Table of n, a(n) for n=0..38.

Eric Weisstein's World of Mathematics, Infinite Cosine Product Integral.

Example

0.785380557298632873492583011467332524761...

Mathematica

(* This naive script is not suitable to get more than 10 digits. *)
digits = 10; m0 = 500; dm = 50; Clear[g];
f[n_Integer, m_] := NIntegrate[Product[Cos[x/k], {k, 1, m - 1}]*(((1 - x^2/(2*m^2))*Gamma[1 + m]^2)/(Gamma[1 + m - x/Sqrt[2]]*Gamma[1 + m + x/Sqrt[2]])), {x, n*Pi/2, (n + 1)*Pi/2}];
g[m_] := g[m] = NSum[f[n, m], {n, 0, Infinity}];
Print[g[m0]]; Print[g[m = m0 + dm]];
While[RealDigits[g[m], 10, digits][[1]] != RealDigits[g[m - dm], 10, digits][[1]], m = m + dm; Print[m, " ", RealDigits[g[m], 10, digits][[1]]]];
RealDigits[g[m], 10, digits][[1]] (* Jean-François Alcover, May 19 2016 *)

Crossrefs

Sequence in context: A277053 A370466 A076415 * A216542 A216544 A216546

Adjacent sequences: A190570 A190571 A190572 * A190574 A190575 A190576

Keyword

nonn,cons,more

Author

N. J. A. Sloane, May 12 2011

Status

approved