An asymptotic distribution theory for Eulerian recurrences with applications

Hsien-Kuei Hwang, Hua-Huai Chern, Guan-Huei Duh

We study linear recurrences of Eulerian type of the form \[ P_n(v) = (α(v)n+γ(v))P_{n-1}(v) +β(v)(1-v)P_{n-1}'(v)\qquad(n\ge1), \] with $P_0(v)$ given, where $\alpha (v),\beta (v)$ and $γ(v)…