1. Proof of a conjecture of Z-W Sun on ratio monotonicity.
- Author
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Sun, Brian, Hu, Yingying, and Wu, Baoyindureng
- Subjects
- *
MATHEMATICAL proofs , *NUMBER theory , *CONVEX domains , *CONCAVE functions , *MATHEMATICAL sequences - Abstract
In this paper, we study the log-behavior of a new sequence $\{S_{n}\} _{n=0}^{\infty}$ , 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 $\{S_{n}\}_{n=0}^{\infty}$ and find the sequences $\{S_{n+1}/S_{n}\}_{n=0}^{\infty}$ and $\{\sqrt[n]{S_{n}}\} _{n=1}^{\infty}$ are log-concave. Our results give an affirmative answer to a conjecture of Z-W Sun on the ratio monotonicity of this new sequence. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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