Asymptotic Growth of $(-1{)}^r{\Delta }^r\log \sqrt[n]{\overline{p}(n)/n^{\alpha }}$ and the Reverse Higher Order Turán Inequalities for $\sqrt[n]{\overline{p}(n)/n^{\alpha }}$

Gargi Mukherjee

Let $\overline{p}(n)$ denote the overpartition function. In this paper, we study the asymptotic growth of finite difference of logarithm of $\sqrt[n]{\overline{p}(n)/n^{\alpha }}$ for $\alpha$…