Integral representations and properties of Stirling numbers of the first kind. (English) Zbl 1336.11022
The paper gives 3 integral representations for the Stirling numbers of the first kind. One of the consequences is the non-negativity of an \(m\times m\) determinant that involves Stirling numbers of the first kind. It is also shown that for every fixed \(k\), the sequence \(s(n+k,k){\binom{n+k}{k}}^{-1}\) is logconvex.
Reviewer: László A. Székely (Columbia)
MSC:
| 11B73 | Bell and Stirling numbers |
| 11B83 | Special sequences and polynomials |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
Keywords:
Stirling numbers of the first kind; integral representation; logconvex sequences; majorization; completely monotonic functionReferences:
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