Two-log-convexity of the Catalan-Larcombe-French sequence
نویسندگان
چکیده
منابع مشابه
Two-log-convexity of the Catalan-Larcombe-French sequence
The Catalan-Larcombe-French sequence {Pn}n≥0 arises in a series expansion of the complete elliptic integral of the first kind. It has been proved that the sequence is log-balanced. In the paper, by exploring a criterion due to Chen and Xia for testing 2-log-convexity of a sequence satisfying three-term recurrence relation, we prove that the new sequence {P2 n – Pn–1Pn+1}n≥1 are strictly log-con...
متن کاملTwo Properties of Catalan-Larcombe-French Numbers
Let (P n) be the Catalan-Larcombe-French numbers. The numbers P n occur in the theory of elliptic integrals, and are related to the arithmetic-geometric-mean. In this paper we investigate the properties of the related sequence S n = P n /2 n instead, since S n is an Apéry-like sequence. We prove a congruence and an inequality for P n .
متن کاملSupercongruences for the Catalan-Larcombe-French numbers
In this short note, we develop the Stienstra-Beukers theory of supercongruences in the setting of the Catalan-Larcombe-French sequence. We also give some applications to other sequences. AMS Subject Classification: 11B83, 11B65, 11F30, 33E05
متن کاملOn the Log-Concavity of the Root of the Catalan-Larcombe-French Numbers
Recently, some combinatorial properties for the the Catalan-Larcombe-French numbers have been proved by Sun and Wu, and Zhao. Recently, Z. W. Sun conjectured that the root of the Catalan-Larcombe-French numbers is log-concave. In this paper, we confirm Sun's conjecture by establishing the lower and upper bound for the ratios of the Catalan-Larcombe-French numbers.
متن کاملAsymptotics of a 3F2 polynomial associated with the Catalan-Larcombe-French sequence
The large n behaviour of the hypergeometric polynomial 3F2 ( −n, 1 2 , 1 2 1 2 − n, 1 2 − n ; −1 ) is considered by using integral representations of this polynomial. This 3F2 polynomial is associated with the Catalan-Larcombe-French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2015
ISSN: 1029-242X
DOI: 10.1186/s13660-015-0920-0