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Two-log-convexity of the Catalan-Larcombe-French sequence.
- Source :
-
Journal of Inequalities & Applications . 12/18/2015, Vol. 2015 Issue 1, p1-7. 7p. - Publication Year :
- 2015
-
Abstract
- The Catalan-Larcombe-French sequence $\{P_{n}\}_{n\geq0}$ 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 $\{P^{2}_{n}-P_{n-1}P_{n+1}\}_{n\geq1}$ are strictly log-convex and hence the Catalan-Larcombe-French sequence is strictly 2-log-convex. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CATALAN numbers
*MATHEMATICAL sequences
*CONVEX domains
*COMBINATORICS
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2015
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 111870456
- Full Text :
- https://doi.org/10.1186/s13660-015-0920-0