|
%I #9 Jul 04 2020 04:18:41
%S 7,5,3,3,0,6,0,9,7,6,9,2,1,5,9,0,9,4,6,4,7,9,3,3,8,3,7,1,9,0,9,8,3,4,
%T 9,6,5,5,9,0,4,3,3,3,7,6,8,9,1,6,8,4,4,5,9,8,4,5,7,5,2,1,2,5,1,6,1,9,
%U 8,8,3,8,5,5,6,2,0,0,5,8,6,0,5,2,1,6
%N Decimal expansion of 1 + Integral_{x=0..1} (-1 + Gamma(1+x))/x dx.
%C This constant also equals lim_{n->oo} (- n + Integral_{x=0..1} (Gamma(x)^(n/(n+1)) dx.)
%H MathOverflow, <a href="https://mathoverflow.net/questions/364420/possible-limit-involving-the-gamma-function">Possible limit involving the gamma function</a>
%e constant = 0.75330609769215909464793383719098349655904333768916844598
%t t = 1 + NIntegrate[(Gamma[1 + x] - 1)/x, {x, 0, 1}, WorkingPrecision -> 140]
%t RealDigits[t][[1]]
%o (PARI) 1 + intnum(x=0, 1, (gamma(1+x)-1)/x) \\ _Michel Marcus_, Jul 04 2020
%Y Cf. A335983.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Jul 03 2020
|
