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A020777
Decimal expansion of (-1)*Gamma'(1/4)/Gamma(1/4) where Gamma(x) denotes the Gamma function.
13
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, 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, 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
OFFSET
1,1
REFERENCES
S.J. Patterson, "An introduction to the theory of the Riemann zeta function", Cambridge studies in advanced mathematics no. 14, p. 135, 1995.
LINKS
FORMULA
Gamma'(1/4)/Gamma(1/4) = -EulerGamma - 3*log(2) - Pi/2 where EulerGamma is the Euler-Mascheroni constant (A001620).
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
EXAMPLE
4.2274535333762654080895301460966835773672444387082422716552795595189567958...
MAPLE
evalf(gamma+3*log(2)+Pi/2) ; # R. J. Mathar, Nov 13 2011
MATHEMATICA
EulerGamma + Pi/2 + Log[8] // RealDigits[#, 10, 105][[1]] & (* Jean-François Alcover, Jun 18 2013 *)
N[StieltjesGamma[0, 1/4], 99] (* Peter Luschny, May 16 2018 *)
PROG
(PARI) Euler+3*log(2)+Pi/2
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R) + Pi(R)/2 + Log(8); // G. C. Greubel, Aug 28 2018
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, May 24 2003
STATUS
approved