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Asymptotic estimates for generalized Stirling numbers. (English) Zbl 1093.11504

Summary: Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by P. Flajolet and H. Prodinger [SIAM J. Discrete Math. 12, No. 2, 155–159 (1999; Zbl 0921.05001)]. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range including the classical integral domain.

MSC:

11B73 Bell and Stirling numbers
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)

Citations:

Zbl 0921.05001
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