Proof of a conjecture of Z-W Sun on ratio monotonicity
Abstract In this paper, we study the log-behavior of a new sequence { S n } n = 0 ∞ $\{S_{n}\} _{n=0}^{\infty}$ , which was defined by Z-W Sun. We find that the sequence is log-convex by using the interlacing method. Additionally, we consider ratio log-behavior of { S n } n = 0 ∞ $\{S_{n}\}_{n=0}^{\...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1221-y |
| Summary: | Abstract In this paper, we study the log-behavior of a new sequence { S n } n = 0 ∞ $\{S_{n}\} _{n=0}^{\infty}$ , which was defined by Z-W Sun. We find that the sequence is log-convex by using the interlacing method. Additionally, we consider ratio log-behavior of { S n } n = 0 ∞ $\{S_{n}\}_{n=0}^{\infty}$ and find the sequences { S n + 1 / S n } n = 0 ∞ $\{S_{n+1}/S_{n}\}_{n=0}^{\infty}$ and { S n n } n = 1 ∞ $\{\sqrt[n]{S_{n}}\} _{n=1}^{\infty}$ are log-concave. Our results give an affirmative answer to a conjecture of Z-W Sun on the ratio monotonicity of this new sequence. |
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| ISSN: | 1029-242X |