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Decimal expansion of p_0, a constant associated with the Khintchine inequality in case of random variables with Rademacher distribution.
1

%I #16 Jul 01 2017 02:24:12

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

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

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

%N Decimal expansion of p_0, a constant associated with the Khintchine inequality in case of random variables with Rademacher distribution.

%H G. C. Greubel, <a href="/A249415/b249415.txt">Table of n, a(n) for n = 1..5000</a>

%H Steven R. Finch, <a href="/A000296/a000296.pdf">Moments of sums</a>, April 23, 2004 [Cached copy, with permission of the author]

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Khintchine_inequality">Khintchine inequality</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Rademacher_distribution">Rademacher distribution</a>

%F p_0 is the unique solution of the equation Gamma((p + 1)/2) = sqrt(Pi)/2.

%e 1.8474163360763421293976936897345912119153478325037...

%p Digits := 120; `assuming`([fsolve(GAMMA((p+1)/2) = sqrt(Pi)/2)], [p > 0]) # _Vaclav Kotesovec_, Oct 28 2014

%t p0 = p /. FindRoot[Gamma[(p + 1)/2] == Sqrt[Pi]/2, {p, 1}, WorkingPrecision -> 104]; RealDigits[p0] // First

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Oct 28 2014