Sun's Log-concavity Conjecture on the Catalan–Larcombe–French Sequence

作     者：James J.Y.ZHAO 

作者机构：Center for Applied Mathematics Tianjin University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2016年第32卷第5期

页      面：553-558页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the 863 Program and the National Science Foundation of China 

主　　题：The Catalan-Larcombe-French sequence the Fennessey-Larcombe-French sequence logconcavity three-term recurrence relation 

摘      要：Let {Pn},n≥0 denote the Catalan-Larcombe-French sequence, which naturally came from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence { n√Pn}n≥1, which was originally conjectured by Z. W. Sun. We also obtain the strict log-concavity of the sequence {n√Vn}n≥1, where {Vn}n≥0 is the Fennessey-Larcombe- French sequence arising from the series expansion of the complete elliptic integral of the second kind.