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Zhao, Feng-Zhen
- The Log-Convexity of Cauchy Numbers
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1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, CN
1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, CN
Source
The Journal of the Indian Mathematical Society, Vol 80, No 3-4 (2013), Pagination: 395-403Abstract
In this paper, we investigate the log-convexity of Cauchy numbers. In addition, we discuss the q-log-concavity of some polynomials related to Cauchy numbers.Keywords
Cauchy Numbers, Log-Convexity, Log-Concavity.
- Some Results for the Inverse Moment of the N-Fold Convolution of the Zero-Truncated Negative Binomial Distribution
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1 Department of Mathematics, Shanghai University, Shanghai 200444, IN
1 Department of Mathematics, Shanghai University, Shanghai 200444, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 199-208Abstract
In this paper, we consider the r-th inverse moment of the n-fold convolution of the zero-truncated negative binomial distribution Gr(k; n). We mainly discuss the first and second inverse moments of this distribution. We derive some recursive formulas for Gr(k; n). In particular, we give some asymptotic approximations for the first and second inverse moments of the n-fold convolution of the zero-truncated negative binomial distribution.Keywords
Negative Binomial Distribution, Inverse Moment, Recursive Formulas, Asymptotic Approximation.References
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- The Log-Behavior of the Partial Sum for the Tribonacci Numbers
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The Journal of the Indian Mathematical Society, Vol 84, No 1-2 (2017), Pagination: 143-149Abstract
Let {Tn}n ≥ 0 and {Tn[1]}n ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {Tn}n ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of Tn[1]}n ≥ 1 and the log-balancedness of some sequences involving Tn[1]. In addition, we discuss the monotonicity of some sequences related to Tn[1].Keywords
Fibonacci Sequence, Tribonacci Sequence, Log-Convexity, Log-Concavity, Log-Balancedness, Monotonicity.References
- N. N. Cao and F. Z. Zhao, Some properties of hyper bonacci and hyperlucas numbers, Journal of Integer Sequences, 13 (2010), Article 10.8.8.
- W. Y. C. Chen, J. J. F. Guo and L. X. W. Wang, In nitely logarithmically monotonic combinatorial sequences, Advances in Applied Mathematics, 52 (2014), 99{120.
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- B. Hacene and B. Amine, Combinatorial expressions involving Fibonacci, hyper bonacci, and incomplete Fibonacci numbers, Journal of Integer Sequences, 17 (2014), Article 14.4.3.
- Q. H. Hou, Z. W. Sun and H. M. Wen, On monotonicity of some combinatorial sequences, Publicationes Mathematicae Debrecen, 85 (2014), 285{295.
- J. Li, Z. L. Jiang and F. L. Lu, Determinants, norms, and the spread of circulant matrices with tribonacci and generalized Lucas numbers, Abstract and Applied Analysis 2014, Article ID 381829.
- R. Liu and F. Z. Zhao, On the sums of reciprocal hyper bonacci numbers and hyperlucas numbers, Journal of Integer Sequences, 15 (2012), Article 12.4.5.
- F. Luca and P. Stanica, On some conjectures on the monotonicity of some arithmetical sequences, Journal of Combinatorics and Number Theory, 4 (2012), 115{123.
- Z. W. Sun, Conjectures involving arithmetical sequences, Proceedings of the 6th China-Japan Seminar, S. Kanemitsu, H. Li and J. Liu eds., World Scienti c, Singapore, 2013, 244{258.
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- Y. Wang and B. X. Zhu, Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences, Science China Mathematics, 57 (2014), 2429{2435.
- F. Z. Zhao, The log-behavior of the Catalan-Larcombe-French sequence, International Journal of Number Theory, 10 (2014), 177{182.
- L. N. Zheng, R. Liu and F. Z. Zhao, On the log-concavity of hyper bonacci Numbers and hyperlucas Numbers, Journal of Integer Sequences, 17 (2014), Article 14.1.4.
- Notes on Some Rogers-Ramanujan Type Identities
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Authors
Affiliations
1 Department of Applied Mathematics, Dalian University of Technology, Dalian-116024, CN
1 Department of Applied Mathematics, Dalian University of Technology, Dalian-116024, CN