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The Higher Derivation of the Hurwitz Zeta-function

Received: 17 June 2015     Accepted: 26 June 2015     Published: 14 July 2015
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Abstract

In this paper, the Euler-Maclaurin Summation formula was researched, the purpose of research is to promote the application of the Hurwitz Zeta-function ; Combination method of number theory special a function and Euler-Maclaurin Summation Formula was been used ; By three derivatives of the the Euler-Maclaurin Summation formula , three formulas of Hurwitz Zeta-function were been given.

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.2015040501.12
Page(s) 6-14
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

Hurwitz Zeta-function, Euler Maclauring Summation, Logarithmic Derivative

References
[1] H.M.Srivastava and J.Choi, Seies Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001.
[2] Shigeru Kanemitsu and Haruo Tsukada, Vistas of Special Functions, World Scientific Publishing Co.Pte.Lid.2007
[3] H-L.Li and M.Toda,”Elaboration of Some Results of Srivastava and Choi”. J.Anal.Appl 25(2006),517-533.
[4] Hailong Li,Number Theory and Special Functions, Science Press Beijing 2011”.
[5] Yang Qian-Li, Wang Yong-Xing and Lihai-Long,On Derivate of a Number Theory and It’s Application Mathem Atics in Practice and Theory. Vol.35,No.8 (2005)194-199.
[6] Kanemitsu S, Kumagai H. and Srivastava HM. Some Integral and Asymptotic Formulas Associate with the Hurwitz Zate Function [J] Appl. Mathcomput,2004(1)31-37.
[7] Ishibashi,M. and Kanemitsu, S., Fractional Part Sums and Divisor Function Ⅰ. In: Number Theory and Combinatorics (Japan 1984; eds: J.Akiyama et al.). Singapore: World Sci.1985,pp. 119-183.
[8] Adamchik, V. S., Polygamma functions of negative order. J. Comput. Appl.Math. 100 (1998), 191-199.
[9] Berndt, B. C., On the Hurwitz zeta-function. Rocky Mount. J. Math. 2 (1972),151-157.
[10] Elizalde, E., An asymptotic expansion for the derivative of the generalized Riemann zeta-function. Math. Comput. 47 (1986), 347 - 350.
Cite This Article
  • APA Style

    Qianli Yang. (2015). The Higher Derivation of the Hurwitz Zeta-function. Pure and Applied Mathematics Journal, 4(5-1), 6-14. https://doi.org/10.11648/j.pamj.s.2015040501.12

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    ACS Style

    Qianli Yang. The Higher Derivation of the Hurwitz Zeta-function. Pure Appl. Math. J. 2015, 4(5-1), 6-14. doi: 10.11648/j.pamj.s.2015040501.12

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    AMA Style

    Qianli Yang. The Higher Derivation of the Hurwitz Zeta-function. Pure Appl Math J. 2015;4(5-1):6-14. doi: 10.11648/j.pamj.s.2015040501.12

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  • @article{10.11648/j.pamj.s.2015040501.12,
      author = {Qianli Yang},
      title = {The Higher Derivation of the Hurwitz Zeta-function},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {5-1},
      pages = {6-14},
      doi = {10.11648/j.pamj.s.2015040501.12},
      url = {https://doi.org/10.11648/j.pamj.s.2015040501.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040501.12},
      abstract = {In this paper, the Euler-Maclaurin Summation formula was researched, the purpose of research is to promote the application of the Hurwitz Zeta-function ; Combination method of number theory special a function and Euler-Maclaurin Summation Formula was been used ; By three derivatives of the the Euler-Maclaurin Summation formula , three formulas of Hurwitz Zeta-function were been given.},
     year = {2015}
    }
    

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Author Information
  • Department of Mathematics and Information Science, Weinan Normal University, Weinan, P. R. China

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