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A020777 Decimal expansion of (-1)*Gamma'(1/4)/Gamma(1/4) where Gamma(x) denotes the Gamma function. 9

%I

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

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

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

%N Decimal expansion of (-1)*Gamma'(1/4)/Gamma(1/4) where 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, 1995.

%H G. C. Greubel, <a href="/A020777/b020777.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>

%F Gamma'(1/4)/Gamma(1/4) = -EulerGamma - 3*log(2) - Pi/2 where EulerGamma is the Euler-Mascheroni constant (A001620).

%F Pi = gamma(0,1/4) - gamma(0,3/4) = A020777 - A200134, where gamma(n,x) denotes the generalized Stieltjes constants. - _Peter Luschny_, May 16 2018

%e 4.2274535333762654080895301460966835773672444387082422716552795595189567958...

%p evalf(gamma+3*log(2)+Pi/2) ; # _R. J. Mathar_, Nov 13 2011

%t EulerGamma + Pi/2 + Log[8] // RealDigits[#, 10, 105][[1]] & (* _Jean-Fran├žois Alcover_, Jun 18 2013 *)

%t N[StieltjesGamma[0, 1/4], 99] (* _Peter Luschny_, May 16 2018 *)

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

%o (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R) + Pi(R)/2 + Log(8); // _G. C. Greubel_, Aug 28 2018

%Y Cf. A001620, A200134, A301816.

%K cons,nonn

%O 1,1

%A _Benoit Cloitre_, May 24 2003

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Last modified July 21 04:40 EDT 2019. Contains 325189 sequences. (Running on oeis4.)