A175292 Decimal expansion of the value of Pi*(gamma + log Pi)/2, where gamma is the Euler-Mascheroni constant.

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, 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, 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

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.

Formula

Equals A019669*(A001620 + A053510).

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

Sequence in context: A341318 A332324 A101689 * A277815 A229178 A019667

Adjacent sequences: A175289 A175290 A175291 * A175293 A175294 A175295

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 24 2010

Status

approved