Higher order log-concavity of the overpartition function and its consequences

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