Stirling number representations. (English) Zbl 1086.05008

Branson, David

Discrete Math. 306, No. 5, 478-494 (2006).

Summary: Stirling numbers of the first and second kinds, \(s(n,k)\) and \(S(n,k)\), may be defined by means of recurrence relations together with a set of initial values. This paper discusses the ambiguities that arise within this prescription when \(n\) takes negative values.

MSC:

05A15	Exact enumeration problems, generating functions
11B73	Bell and Stirling numbers

Keywords:

Generating function; Formal power series; Factorial series; Stirling’s formula

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