科研之友
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摘要
Using the Saddle point method and multiseries expansions, we obtain from the generating function of the Stirling numbers of the second kind {(n) (m)} and Cauchy's integral formula, asymptotic results in central and non-central regions. In the central region, we revisit the celebrated Gaussian theorem with more precision. In the region m = n - n(alpha), 1 > alpha > 1/2, we analyze the dependence of {(n) (m)} on alpha. An extension of some Moser and Wyman's result to full m range is also provided. This paper fits within the framework of Analytic Combinatorics.
- 出版日期2013-10
