Formulae for Euler’s gamma without logarithm

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.