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

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• 作者：Aimin Xu ^{xuaimin1009@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11Y60 ; 41A60
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：163
• 期：Complete
• 页码：255-266
• 全文大小：296 K

文摘

Based on the Bell polynomials, Chen and Lin (2013) [9] obtained explicitly the coefficients a_m$a_m$(m=1,2,…)$(m=1,2,\dots )$ in the following asymptotic expansion related to the Glaisher–Kinkelin constant A: 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.