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

作　　者：James J.Y.ZHAO 

机构地区：[1]Center for Applied Mathematics, Tianjin University

出　　处：《Acta Mathematica Sinica,English Series》2016年第5期553-558,共6页数学学报（英文版）

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

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.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.

关 键 词：The Catalan-Larcombe-French sequence the Fennessey-Larcombe-French sequence logconcavity three-term recurrence relation 

分 类 号：O156[理学—数学]