Asymptotic expansions related to the Glaisher–Kinkelin constant and its analogues

Based on the Bell polynomials, Chen and Lin (2013) [9] obtained explicitly the coefficients amam(m=1,2,…)(m=1,2,…) in the following asymptotic expansion related to the Glaisher–Kinkelin constant A:1122⋯nn∼A⋅nn22+n2+112e−n24(∑m=0∞amnm)1/r. In this paper, we provide a recurrence formula for the computation of these coefficients, and further describe their asymptotic behavior. We also give recurrence formulas, explicit expressions and asymptotic formulas for the coefficients of similar approximation formulas for two analogues of the Glaisher–Kinkelin constant.