A247377 - OEIS

%I #21 Nov 05 2023 14:15:19

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

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

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

%N Decimal expansion of Integral_{0..oo} 1/Gamma(1+x) dx, a variation of the Fransén-Robinson constant.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 263.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Fransen-RobinsonConstant.html">Fransén-Robinson Constant</a>

%F Also equals e - Integral_{-oo..oo}  e^(-e^x)/(x^2 + Pi^2) dx (observed by Ramanujan).

%e 2.266534507699848835071963857678220918408829714280222193861...

%t NIntegrate[1/Gamma[1 + x], {x, 0, Infinity}, WorkingPrecision -> 104] // RealDigits // First

%o (Python)

%o from mpmath import *

%o mp.dps = 200

%o A247377 = [d for d in nstr(quad(lambda x:1/gamma(1+x),[0,inf]),n=mp.dps)[:-1] if d != '.'] # _Chai Wah Wu_, Sep 16 2014

%o (PARI)

%o localprec(100); intnum(x=0,[[1], 1],1/gamma(1+x)) \\ _Dumitru Damian_, Oct 12 2023

%Y Cf. A058655.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, Sep 15 2014