Log-concavity of P-recursive sequences

摘要

We consider the higher order Turan inequality and higher order log-concavity for sequences {a(n)}(n = 0) such thatan-1a(n+1)/a(n)(2) =1+ Sigma(m)(i=1) ri(log n)/n(alpha i) + o , (1/n(beta)),where m is a nonnegative integer, alpha(i) are real numbers, r(i)(x) are rational functions of x and0 alpha(1) alpha(2) . . . alpha(m) beta.We will give a sufficient condition on the higher order Turan inequality and the t-log-concavity for n sufficiently large. Many P-recursive sequences fall in this frame. At last, we will give a method to find the N such that for any n N, the higher order Turan inequality holds. (C) 2021 Elsevier Ltd. All rights reserved.