Abstract
The problem of the approximation to the Euler constant γ is considered. Some new formulas for the computation of Euler's constant are suggested. The problem of fast evaluation of γ is discussed.
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References
H. Alzer, Inequalities for the gamma and polygamma functions, Abh. Math. Sem. Univ. Hamburg 68 (1998) 363–372.
A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, eds., Higher Transcendental Functions, Bateman Manuscript Project (McGraw-Hill, New York, 1953).
D.W. DeTemple, A quicker convergence to Euler's constant, Amer. Math. Monthly 100(5) (1993) 468–470.
G.M. Fichtenholz, Differential-und Integralrechnung, Vol. 2 (VEB Deutscher Verlag der Wissenschaften, Berlin, 1964).
A.A. Karatsuba and S.M. Voronin, The Riemann Zeta-Function (W. de Gruyter, Berlin, 1992).
E.A. Karatsuba, Fast evaluations of transcendental functions, Problemy Peredachi Informatsii 27(4) (1991) 87–110.
E.A. Karatsuba, Fast calculation of ?(3), Problems Inform. Transmission 29(1) (1993) 58–62.
E.A. Karatsuba, Fast evaluation of Bessel functions, Integral Transforms Special Functions 1(4) (1993) 269–276.
E.A. Karatsuba, Fast calculation of the Riemann zeta function ?(s) for integer values of the argument s, Problems Inform. Transmission 31(4) (1995) 353–362.
E.A. Karatsuba, Fast computation of the values of Hurwitz zeta function and Dirichlet L-series, Problems Inform. Transmission 34(4) (1998) 342–353.
E.A. Karatsuba, Fast evaluation of hypergeometric function by FEE, in: Proc. of the 3rd CMFT Conf. on Computational Methods and Function Theory 1997, eds. N. Papamichael, St. Ruscheweyh and E.B. Saff, Series in Approximation and Decomposition (World Scientific, Singapore, 1999) pp. 303–314.
S.R. Tims and J.A. Tyrell, Approximate evaluation of Euler's constant, Math. Gaz. 55 (1971) 65–67.
E.T. Whittaker and G.N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, London, 1958).
R.M. Young, Euler's constant, Math. Gaz. 75(472) (1991) 187–190.
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Karatsuba, E.A. On the computation of the Euler constant γ. Numerical Algorithms 24, 83–97 (2000). https://doi.org/10.1023/A:1019137125281
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DOI: https://doi.org/10.1023/A:1019137125281