Asymptotic r-log-convexity and P-recursive sequences

Add time:07/13/2019    Source:sciencedirect.com

Let L be the operator given by L{an}n≥0={an+12−anan+2}n≥0. A sequence {an}n≥0 is called asymptotically r-log-convex if Lk{an}n≥N are non-negative sequences for 1≤k≤r and a certain integer N. Based on asymptotic analysis, we present a method for proving the asymptotic r-log-convexity of a sequence. As an application, we consider the problem of proving the asymptotic r-log-convexity of P-recursive sequences. We find that most P-recursive sequences are asymptotically r-log-convex for any non-negative integer r once they are asymptotically log-convex. Moreover, we show how to find an explicit integer N such that they are r-log-convex for n≥N.

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