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Erschienen in:
2002 | OriginalPaper | Buchkapitel
Concavity Properties and a Generating Function for Stirling Numbers
verfasst von : Elliott H. Lieb
Erschienen in: Inequalities
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The Stirling numbers of the first kind, SNk, and of the second kind, σNk, are shown to be strongly logarithmically concave as functions of k for fixed TV. This result is stronger than the unimodality conjecture which was heretofore proved only for σNk (Harper). We also introduce a generating function for the σNk which is different from the conventional one but which has a relatively simple closed form expression.