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 A070860 Decimal expansion of (-1)*c(1) where, in a neighborhood of zero, Gamma(x) = 1/x + c(0) + c(1)*x + c(2)*x^2 + ... (Gamma(x) denotes the Gamma function). 1

%I

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

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

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

%N Decimal expansion of (-1)*c(1) where, in a neighborhood of zero, Gamma(x) = 1/x + c(0) + c(1)*x + c(2)*x^2 + ... (Gamma(x) denotes the Gamma function).

%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="/A070860/b070860.txt">Table of n, a(n) for n = 0..10000</a>

%F c(1) = (EulerGamma^2 - zeta(2))/2 = -0.65587807152025388... ( c(0) = -EulerGamma where EulerGamma is the Euler-Mascheroni constant (A001620)).

%e 0.65587807152025388107701951514539048127976638047858434729236244568387...

%t RealDigits[(Zeta[2] - EulerGamma^2)/2, 10, 100][[1]] (* _G. C. Greubel_, Sep 05 2018 *)

%o (PARI) -(Euler^2-zeta(2))/2

%o (MAGMA) R:= RealField(100); (Pi(R)^2 - 6*EulerGamma(R)^2)/12; // _G. C. Greubel_, Sep 05 2018

%K cons,nonn

%O 0,1

%A _Benoit Cloitre_, May 24 2003

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)