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A047787 Decimal expansion of (-1)*Gamma'(1/3)/Gamma(1/3) where Gamma(x) denotes the Gamma function. 12

%I

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

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

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

%N Decimal expansion of (-1)*Gamma'(1/3)/Gamma(1/3) where Gamma(x) denotes the Gamma function.

%C Decimal expansion of -psi(1/3). - _Benoit Cloitre_, Mar 07 2004

%D S. J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135

%H G. C. Greubel, <a href="/A047787/b047787.txt">Table of n, a(n) for n = 1..10000</a>

%F Gamma'(1/3)/Gamma(1/3)=-EulerGamma-(3/2)*log(3)-Pi/(2*sqrt(3))=-3.13203378002... where EulerGamma is the Euler-Mascheroni constant (A001620).

%t RealDigits[PolyGamma[1/3], 10, 105] // First (* _Jean-Fran├žois Alcover_, Aug 08 2015 *)

%o (PARI) Euler+(3/2)*log(3)+Pi/(2*sqrt(3))

%o (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField();

%o EulerGamma(R) + (3/2)*Log(3) + Pi(R)/(2*Sqrt(3)); // _G. C. Greubel_, Aug 28 2018

%K cons,nonn

%O 1,1

%A _Benoit Cloitre_, May 24 2003

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Last modified February 20 21:15 EST 2020. Contains 332084 sequences. (Running on oeis4.)