Two-log-convexity of the Catalan-Larcombe-French sequence
| Autor: | Sun, Brian Yi, Wu, Baoyindureng |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1186/s13660-015-0920-0 |
| Popis: | The Catalan-Larcombe-French sequence $\{P_n\}_{n\geq 0}$ 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 $\{P^2_n-P_{n-1}P_{n+1}\}_{n\geq 1}$ are strictly log-convex and hence the Catalan-Larcombe-French sequence is strictly 2-log-convex. Comment: 8 pages in Journal of Inequality and Applications,2015 |
| Databáze: | arXiv |
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