OFFSET
1,1
COMMENTS
The absolute value of the integral of sin(Pi*x)*log(x)/x from x=0 to infinity.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
I. Gradsteyn, I. Ryzhik, Table of integrals, series and products, (1981) [4.421.1].
R. J. Mathar, Numerical evaluation of the oscillatory integral over exp(i*pi*x)*x^(1/x) between 1 and infinity, arXiv:0912.3844 [math.CA], 2009-2010, App. B.
EXAMPLE
2.7048257460603808488495681414587002002384217355632...
MAPLE
evalf(Pi*(gamma+log(Pi))/2) ;
MATHEMATICA
RealDigits[Pi*(EulerGamma + Log[Pi])/2, 10, 100][[1]] (* G. C. Greubel, Sep 06 2018 *)
PROG
(PARI) default(realprecision, 100); Pi*(Euler + log(Pi))/2 \\ G. C. Greubel, Sep 06 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)*(EulerGamma(R) + Log(Pi(R)))/2; // G. C. Greubel, Sep 06 2018
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Mar 24 2010
STATUS
approved