A175292 - OEIS

%I #11 Sep 08 2022 08:45:51

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

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

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

%N Decimal expansion of the value of Pi*(gamma + log Pi)/2, where gamma is the Euler-Mascheroni constant.

%C The absolute value of the integral of sin(Pi*x)*log(x)/x from x=0 to infinity.

%H G. C. Greubel, <a href="/A175292/b175292.txt">Table of n, a(n) for n = 1..10000</a>

%H I. Gradsteyn, I. Ryzhik, <a href="http://mathtable.com/gr/index.html">Table of integrals, series and products</a>, (1981) [4.421.1].

%H R. J. Mathar, <a href="http://arxiv.org/abs/0912.3844">Numerical evaluation of the oscillatory integral over exp(i*pi*x)*x^(1/x) between 1 and infinity</a>, arXiv:0912.3844 [math.CA], 2009-2010, App. B.

%F Equals A019669*(A001620 + A053510).

%e 2.7048257460603808488495681414587002002384217355632...

%p evalf(Pi*(gamma+log(Pi))/2) ;

%t RealDigits[Pi*(EulerGamma + Log[Pi])/2, 10, 100][[1]] (* _G. C. Greubel_, Sep 06 2018 *)

%o (PARI) default(realprecision, 100); Pi*(Euler + log(Pi))/2 \\ _G. C. Greubel_, Sep 06 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*(EulerGamma(R) + Log(Pi(R)))/2; // _G. C. Greubel_, Sep 06 2018

%K cons,easy,nonn

%O 1,1

%A _R. J. Mathar_, Mar 24 2010