The Log-Behavior of the Sequence for the Partial Sum of a Log-Convex Sequence

Abstract

In this paper, we study the log-behavior of the partial sum for a log-convex sequence. We prove that the log-convexity of the partial sum for a log-convex sequence is preserved under a mild condition. As applications, we mainly discuss the log-convexity of the partial sums for many famous combinatorial sequences.