Asymptotic expansions related to hyperfactorial function and Glaisher–Kinkelin constant

摘要

In this paper, by the Bernoulli numbers and the exponential complete Bell polynomials, we establish two general asymptotic expansions related to the hyperfactorial function and the Glaisher–Kinkelin constant, where the coefficients in the series of the expansions can be determined by recurrences. Moreover, the explicit expressions of the coefficients are studied and some special asymptotic expansions are presented.