Two-log-convexity of the Catalan-Larcombe-French sequence
نویسندگان
چکیده
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 {P2 n – 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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