On Log-concavity of a Class of Generalized Stirling Numbers
Keywords: Stirling numbers, log-concavity, log-convexity, $q$-log-concavity, $q$-log-convexity
AbstractThis paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are $q$-log-concave or $q$-log-convex under suitable conditions. We further discuss the log-convexity of some linear transformations related to generalized Stirling numbers of the first kind.