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A190573
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Decimal expansion of Integral_{x = 0 to oo} Product_{m=1..oo} cos(x/m) dx.
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1
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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
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OFFSET
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0,1
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REFERENCES
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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.
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LINKS
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EXAMPLE
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0.785380557298632873492583011467332524761...
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MATHEMATICA
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(* 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]]]];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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