Concavity Properties and a Generating Function for Stirling Numbers

Elliott H. Lieb
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Elliott H. Lieb: Northeastern University, Physics Department

A chapter in Inequalities, 2002, pp 109-112 from Springer

Abstract: Abstract The Stirling numbers of the first kind, S N k, and of the second kind, σN k, 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 σN k (Harper). We also introduce a generating function for the σN k which is different from the conventional one but which has a relatively simple closed form expression.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_12

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DOI: 10.1007/978-3-642-55925-9_12

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