Abstract
A number of new formulas and an asymptotic expansion for the Euler–Mascheroni constant γ not containing logarithm are obtained. The accuracy of approximations for the constant by the partial sums of the asymptotic expansion is evaluated. It is conceivable that these formulas and the asymptotic expansion will be helpful in working out algorithms for high-precision computation of the constant in shortening the computation time and in analysis of the irrationality of the constant γ.
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References
R.P. Brent and E.M. McMillan, Some new algorithms for high-precision computation of Euler’s constant, Math. Comput., 34(149):305–312, 1980.
G.M. Fikhtengol’ts, A Course of Differential and Integral Calculus, Vol. 2, Fizmatlit, Moscow, 2001 (in Russian).
X. Gourdon and P. Sebah, Collection of formulas for Euler’s constant γ, available from: http://numbers.computation.free.fr/Constants/constants.html.
X. Gourdon and P. Sebah, The Euler constant: γ, available from: http://numbers.computation.free.fr/Constants/Gamma/gamma.html.
J.J. Mačys, On the Euler–Mascheroni constant, Math. Notes, 94(5):645–652, 2013.
J.J. Mačys and J. Sušinskas, Accuracy of new formulas for the Euler–Mascheroni constant, Matematika ir matematinis modeliavimas, 10, 2014 (forthcomming).
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Mačys, J.J., Banys, R. Formulae for Euler’s gamma without logarithm. Lith Math J 54, 463–470 (2014). https://doi.org/10.1007/s10986-014-9257-5
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DOI: https://doi.org/10.1007/s10986-014-9257-5