Let ${\overline{p}}(n)$ denote the overpartition function. In this paper, we study the asymptotic higher-order log-concavity property of the overpartition function in a similar framework done by Hou and Zhang for the partition function. This will enable us to move on further in order to prove log-concavity of overpartitions, explicitly by studying the asymptotic expansion of the quotient ${\overline{p}}(n-1){\overline{p}}(n+1)/{\overline{p}}(n)^2$ up to a certain order. This enables us to additionally prove 2-log-concavity and higher Turán inequalities with a unified approach.

Let p(n) denote the overpartition function. In this paper, we study the asymptotic higher order log-concavity property of the overpatition function in a similar framework done by Hou and Zhang for the partition function. This will enable us to move on further in order to prove log-concavity of overpartitions, explicitly by studying the asymptotic expansion of the quotient p(n − 1)p(n + 1)/p(n) 2 upto a certain order so that one can finally ends up with the phenomena of 2-log-concavity and higher order Turán property of p(n) by following a sort of unified approach.