Asymptotic r-log-convexity and P-recursive sequences

作者：Hou, Qing-Hu^*; Zhang, Zuo-Ru

来源：Journal of Symbolic Computation, 2019, 93: 21-33.

DOI：10.1016/j.jsc.2018.04.012

• r-Log-convexity
• P-recursive sequence
• Asymptotic expansion

Let L be the operator given by L{a(n)}(n >= 0) = (a(n+)1(2) - a(n)a(n+2))(n >= 0). A sequence {a(n)}(n >= 0) is called asymptotically r-log-convex if L-k{a(n)}(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.

• 出版日期2019-8
• 单位天津大学