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A175292 Decimal expansion of the value of Pi*(gamma + log Pi)/2, where gamma is the Euler-Mascheroni constant. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A200680 A260129 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

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Last modified November 18 22:39 EST 2019. Contains 329305 sequences. (Running on oeis4.)