### The Higher Derivation of the Hurwitz Zeta-function

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

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.
• 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

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

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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title = {The Higher Derivation of the Hurwitz Zeta-function},
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volume = {4},
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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.},
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Author Information
• Department of Mathematics and Information Science, Weinan Normal University, Weinan, P. R. China

• Sections