%I #18 Mar 29 2024 10:58:38

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

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

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

%N Decimal expansion of integral_{0..infinity} exp(-x^2)*log(x) dx.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5 Euler-Mascheroni constant, p. 31, 1.5.2 Integrals.

%H G. C. Greubel, <a href="/A247017/b247017.txt">Table of n, a(n) for n = 0..5000</a>

%F Equals -(1/4)*sqrt(Pi)*(EulerGamma + 2*log(2)).

%e -0.87005772672831550673464879953608743750810733362594...

%t RealDigits[-(1/4)*Sqrt[Pi]*( EulerGamma + 2*Log[2]), 10, 102] // First

%t RealDigits[NIntegrate[Exp[-x^2]Log[x],{x,0,\[Infinity]},WorkingPrecision->120],10,120][[1]] (* _Harvey P. Dale_, Mar 29 2024 *)

%o (PARI) -(1/4)*sqrt(Pi)*(Euler + 2*log(2)) \\ _Michel Marcus_, Sep 09 2014

%Y Cf. A020759.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Sep 09 2014