Log-concavity of P-recursive sequences. (November 2021)

• Record Type: Journal Article
• Authors: Hou, Qing-hu; Li, Guojie
• Is Part Of: Journal of symbolic computation. Volume 107(2021)
• Page Start: 251
• Page End: 268
• Publication Date: 2021-11
• Subjects: 41A60 -- 05A20 -- 41A58; Higher order Turán inequality -- Log-concave -- P-recursive sequence -- Asymptotic estimation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2021.03.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We consider the higher order Turán inequality and higher order log-concavity for sequences { a n } n ≥ 0 such that a n − 1 a n + 1 a n 2 = 1 + ∑ i = 1 m r i ( log ⁡ n ) n α i + o ( 1 n β ), where m is a nonnegative integer, α i are real numbers, r i ( x ) are rational functions of x and 0 < α 1 < α 2 < ⋯ < α m < β . We will give a sufficient condition on the higher order Turán inequality and the ℓ -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 Turán inequality holds.