Two-log-convexity of the Catalan-Larcombe-French sequence

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• 作者：Brian Y Sun ; Baoyindureng Wu
• 关键词：log ; balanced sequence ; log ; convex sequence ; log ; concave sequence ; the Catalan ; Larcombe ; French sequence ; three ; term recurrence
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,474 KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

The Catalan-Larcombe-French sequence \(\{P_{n}\}_{n\geq0}\) 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 \(\{P^{2}_{n}-P_{n-1}P_{n+1}\}_{n\geq1}\) are strictly log-convex and hence the Catalan-Larcombe-French sequence is strictly 2-log-convex.