We define the Stirling numbers for complex values and obtain extensions of certain identities involving these numbers. We also show that the generalization is a natural one for proving unimodality and monotonicity results for these numbers. The definition is based on the Cauchy integral formula and can be used for many other combinatorial numbers
Stirling numbers for complex arguments / B. RICHMOND; D. MERLINI. - In: SIAM JOURNAL ON DISCRETE MATHEMATICS. - ISSN 0895-4801. - STAMPA. - 10:(1997), pp. 73-82. [10.1137/S0895480195284329]
Stirling numbers for complex arguments
MERLINI, DONATELLA
1997
Abstract
We define the Stirling numbers for complex values and obtain extensions of certain identities involving these numbers. We also show that the generalization is a natural one for proving unimodality and monotonicity results for these numbers. The definition is based on the Cauchy integral formula and can be used for many other combinatorial numbers
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