On Non-central Stirling Numbers of the First Kind

Details On Non-central Stirling Numbers of the First Kind On Non-central Stirling Numbers of the First Kind

2009-01-17

arxiv.org/abs/0901.2655v1

Mathematics

Combinatorics

Scientific paper

It is shown in this note that non-central Stirling numbers s(n,k,a) of the first kind naturally appear in the expansion of derivatives of the product of a power function and a logarithn function. We first obtain a recurrence relation for these numbers, and then, using Leibnitz rule we obtain an explicit formula for these numbers. We also obtain an explicit formula for s(n,1,a), and then derive several combinatorial identities related to these numbers.

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