Concavity Properties and a Generating Function for Stirling Numbers
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.
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