Unified treatment of several asymptotic expansions concerning some mathematical constants

摘要

Recently various approximation formulas for some mathematical constants have been investigated and presented by many authors. In this paper, we first find that the relationship between the coefficients pj and qj is such that ψ(x∑j=0∞qjx−j)∼ln(x∑j=0∞pjx−j),x→∞,where ψ is the logarithmic derivative of the gamma function (often referred to as psi function) and p0=q0=1. Next, by using this result, we give a unified treatment of several asymptotic expansions concerning the Euler–Mascheroni constant, Landau and Lebesgue constants, Glaisher–Kinkelin constant, and Choi–Srivastava constants.