Concavity properties and a generating function for stirling numbers

AbstractThe Stirling numbers of the first kind, SNk, and of the second kind, δNk, are shown to be strongly logarithmically concave as functions of k for fixed N. This result is stronger than the unimodality conjecture which was heretofore proved only for δNk (Harper). We also introduce a generating function for the δNk which is different from the conventional one but which has a relatively simple closed form expression