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On The Parameter Function Involving Gamma Function and Its Applications

Received: 18 June 2015     Accepted: 11 July 2015     Published: 25 July 2015
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Abstract

In this paper, the complete monotonic parameter function involving the Gamma function is considered. The necessary and sufficient condition of the parameter f is presented. As an application, two meaningful inequalities of Gamma function are obtained

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 5-1)

This article belongs to the Special Issue Mathematical Aspects of Engineering Disciplines

DOI 10.11648/j.pamj.s.2015040501.14
Page(s) 20-23
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Gamma function, Completely Monotonicity, Inequalities

References
[1] W. Magnus, F. Oberhettinger, R.P. Soni. Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag, Berlin, 1966.
[2] D. Kershaw, A. Laforgia. Monotonicity results for the gamma function .Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.1985, 119:127-133.
[3] Zh.-X. Wang, D.-R. Guo.Special Functions .World Scientific, Singapore, 1989.translated into Chinese by D.-R. Guo, X.-J. Xia.
[4] Ch.-P.Chen. Some properties of functions related to the gamma, psi and tetragamma functions. Computers and Mathematics with Applications.2011,62:3389–3395.
[5] Ch.-P.Chen. Some properties of functions related to the gamma, psi and tetragamma functions. Computers and Mathematics with Applications.2011, 62:3389-3395.
[6] Bin Chen. Some properties on the function involving the Gamma function. Applied Mathematics. 2012, 3(6): 587-589.
[7] Bin Chen. Research on equation involving two new functions on information security. Journal of Convergence Information Technology. 2013,8(8) :284-291.
[8] Chao-Ping Chen,Long Lin.Remarks on asymptotic expansions for the gamma function. Applied Mathematics Letters. 2012,25: 2322–2326.
[9] Bin Chen, Haigang Zhou. Note on the problem of Ramanujan radial limits,Advances in difference equations. 2014,191:1-11.
[10] Bin Chen. A new equation involving the Euler function. 2010 IEEE International Conference on Information Theory and Information Security. 2010,12:121-125.
Cite This Article
  • APA Style

    Bin Chen, Rong Miao. (2015). On The Parameter Function Involving Gamma Function and Its Applications. Pure and Applied Mathematics Journal, 4(5-1), 20-23. https://doi.org/10.11648/j.pamj.s.2015040501.14

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    ACS Style

    Bin Chen; Rong Miao. On The Parameter Function Involving Gamma Function and Its Applications. Pure Appl. Math. J. 2015, 4(5-1), 20-23. doi: 10.11648/j.pamj.s.2015040501.14

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    AMA Style

    Bin Chen, Rong Miao. On The Parameter Function Involving Gamma Function and Its Applications. Pure Appl Math J. 2015;4(5-1):20-23. doi: 10.11648/j.pamj.s.2015040501.14

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  • @article{10.11648/j.pamj.s.2015040501.14,
      author = {Bin Chen and Rong Miao},
      title = {On The Parameter Function Involving Gamma Function and Its Applications},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {5-1},
      pages = {20-23},
      doi = {10.11648/j.pamj.s.2015040501.14},
      url = {https://doi.org/10.11648/j.pamj.s.2015040501.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040501.14},
      abstract = {In this paper, the complete monotonic parameter function involving the Gamma function is considered. The necessary and sufficient condition of the parameter f is presented. As an application, two meaningful inequalities of Gamma function are obtained},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - On The Parameter Function Involving Gamma Function and Its Applications
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    AU  - Rong Miao
    Y1  - 2015/07/25
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    DO  - 10.11648/j.pamj.s.2015040501.14
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
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    AB  - In this paper, the complete monotonic parameter function involving the Gamma function is considered. The necessary and sufficient condition of the parameter f is presented. As an application, two meaningful inequalities of Gamma function are obtained
    VL  - 4
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Author Information
  • Department of mathematics and information science, Weinan Normal University, ShaanXi, China

  • Department of mathematics and information science, Weinan Normal University, ShaanXi, China

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