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 se...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.展开更多
基金Supported by the 863 Program and the National Science Foundation of China
文摘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.
