# Eulerian numbers with fractional order parameters

@article{Butzer1992EulerianNW, title={Eulerian numbers with fractional order parameters}, author={P. L. Butzer and Michael Hauss}, journal={aequationes mathematicae}, year={1992}, volume={46}, pages={119-142} }

SummaryThe aim of this paper is to generalize the well-known “Eulerian numbers”, defined by the recursion relationE(n, k) = (k + 1)E(n − 1, k) + (n − k)E(n − 1, k − 1), to the case thatn ∈ ℕ is replaced by α ∈ ℝ. It is shown that these “Eulerian functions”E(α, k), which can also be defined in terms of a generating function, can be represented as a certain sum, as a determinant, or as a fractional Weyl integral. TheE(α, k) satisfy recursion formulae, they are monotone ink and, as functions of…

## 13 Citations

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This article is a short review of the recent results on properties of nonlinear fractional maps which are maps with power- or asymptotically power-law memory. These maps demonstrate the new type of…

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