Two-log-convexity of the Catalan-Larcombe-French sequence
Abstract
The Catalan-Larcombe-French sequence \Pn\n≥ 0 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 \P2n-Pn-1Pn+1\n≥ 1 are strictly log-convex and hence the Catalan-Larcombe-French sequence is strictly 2-log-convex.
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