Asymptotic expansion of the arithmetic-geometric mean is obtained and it is used to analyze inequalities and relations between arithmetic-geometric mean and other classical means. Mathematics subject… (More)

In this paper various approximations for the Euler–Mascheroni constant and harmonic numbers are studied and improved and general asymptotic expansions related to this approximations are obtained.… (More)

The Hermite-Hadamard inequality is used to develop an approximation to the logarithm of the gamma function which is more accurate than the Stirling approximation and easier to derive. Then the… (More)

Complete monotonicity properties of some functions involving the psi function are studied and some known results are extended and generalized. Moreover, a necessary and sufficient conditions for some… (More)

We derive algorithms for computing asymptotic expansion of the composite mean of two arbitrary means M and N . Then we analyse asymptotic behaviour of the compound mean M N . Examples and application… (More)