Sun's log-concavity conjecture on the Catalan-Larcombe-French sequence

Let {P n } 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 {Pn...n}n.1, which was originally conjectured by Z. W. Sun. We also obtain the strict log-concavity of the sequence {Vn...n}n.1, where {V n } n.0 is the Fennessey.Larcombe.French sequence arising from the series expansion of the complete elliptic integral of the second kind.