A273051 - OEIS

%I #14 Jan 17 2020 16:30:45

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

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

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

%N Decimal expansion of the second 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 MathWorld <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^2/gamma(x) dx where I = Integral_{x>=0} 1/gamma(x) dx is the Fransén-Robinson constant.

%e 4.83648597463342689473636069232113892436851608107360722903294224216...

%t digits = 101;

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

%t M2 = (1/I0) NIntegrate[x^2/Gamma[x], {x, 0, Infinity}, WorkingPrecision -> digits + 5];

%t RealDigits[M2, 10, digits][[1]]

%o (PARI) default(realprecision, 120); intnum(x=0, [[1], 1], x^2/gamma(x))/intnum(x=0, [[1], 1], 1/gamma(x)) \\ _Vaclav Kotesovec_, May 14 2016

%Y Cf. A058655, A273017.

%K nonn,cons

%O 1,1

%A _Jean-François Alcover_, May 14 2016