Logarithmically complete monotonicity properties and characterizations of the gamma function

Authors

  • Ai-Jun Li
  • Chao-Ping Chen

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.65

Abstract

n this paper, the logarithmically complete monotonic properties of the functions $ \prod_{i=1}^{n}\frac{\Gamma(x-a_i)}{\Gamma(x-b_i)} $ ,$ \Gamma(x)^{\alpha}\Gamma\Big(x-\sum_{i=1}^n a_i\Big)/\prod_{i=1}^{n}\Gamma(x-a_i) $, and $ x^r(e/x)^x \Gamma(x) $ are obtained. Some characterizations of the gamma function are deduced.

Author Biographies

Ai-Jun Li

Department of Mathematics, Shanghai University, Shanghai 200444, China.

Chao-Ping Chen

School of Mathematics and Informatics, Research Institute of Applied Mathematics, Henan Polytechnic University, Jiaozuo City, Henan 454010, China.

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Published

2007-12-31

How to Cite

Li, A.-J., & Chen, C.-P. (2007). Logarithmically complete monotonicity properties and characterizations of the gamma function. Tamkang Journal of Mathematics, 38(4), 313-322. https://doi.org/10.5556/j.tkjm.38.2007.65

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Section

Papers