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- Publisher
- Springer Journals
- Copyright
- Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2020
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-020-0952-1
- Publisher site
- See Article on Publisher Site
Abstract
Two interesting sequences arose in the study of the series expansions of the complete elliptic integrals, which are called the Catalan-Larcombe-French sequence {Pn}n≥0 and the Fennessey-Larcombe-French sequence {Vn}n>0 respectively. In this paper, we first establish some criteria for determining log-behavior of a sequence based on its three-term recurrence. Then we prove the log-convexity of {Vn2 − Vn−1Vn+1}n≥2 and {n!Vn}n≥1, the ratio log-concavity of {Pn}n≥0 and the sequence {An}n≥0 of Apéry numbers, and the ratio log-convexity of {Vn}n≥1.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 2, 2020