A273017 - OEIS

%I #19 Mar 08 2023 05:15:18

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

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

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

%N Decimal expansion of the first moment of the reciprocal gamma distribution.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 262.

%H Steven R. Finch <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a> p. 35.

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Reciprocal_gamma_function">Reciprocal gamma function</a>

%F (1/I)*Integral_{x>=0} x/gamma(x) dx where I = Integral_{x>=0} 1/gamma(x) dx is the Fransén-Robinson constant.

%e 1.93456704214788472118371470436917892438217559226658848385544754...

%t digits = 100;

%t I0 = NIntegrate[1/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];

%t M1 = (1/I0) NIntegrate[x/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];

%t RealDigits[M1, 10, digits][[1]]

%o (PARI) default(realprecision, 120); intnum(x=0, [[1], 1], x/gamma(x))/intnum(x=0, [[1], 1], 1/gamma(x)) \\ _Vaclav Kotesovec_, May 14 2016

%Y Cf. A058655.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, May 13 2016