OFFSET
1,1
COMMENTS
See A087132.
LINKS
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 42.
Ph. Flajolet, É. Fusy, X. Gourdon, D. Panario, N. Pouyanne, A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics, arXiv:math/0606370 [math.CO]
FORMULA
prod_{k>=1} I_0(2/k), where I_0 is the zeroth modified Bessel function.
EXAMPLE
4.2634035141526697782989350551661966905350818174794...
MAPLE
evalf(product(BesselI(0, 2/k), k=1..infinity), 100) # Vaclav Kotesovec, Sep 17 2014
MATHEMATICA
digits = 50; m0 = 1000; dm = 1000; tail[m_] := PolyGamma[1, m] - (1/24)*PolyGamma[3, m] + PolyGamma[5, m]/1080 - (11*PolyGamma[7, m])/967680 + (19*PolyGamma[9, m])/217728000 - (43*PolyGamma[11, m])/94058496000; Clear[f]; f[m_] := f[m] = Sum[Log[BesselI[0, 2/k]], {k, 1, m - 1}] + tail[m] // N[#, digits + 5] &; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits + 2] != RealDigits[f[m - dm], 10, digits + 2], Print["f(", m, ") = ", f[m]]; m = m + dm]; RealDigits[Exp[f[m]], 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 08 2014
EXTENSIONS
More terms from Vaclav Kotesovec, Sep 17 2014
STATUS
approved