Russian Journal of Mathematical Physics

, Volume 17, Issue 4, pp 495–508 | Cite as

Special functions related to Dedekind-type DC-sums and their applications

Article

Abstract

In this paper, we construct trigonometric functions in the form of a sum T p (h, k) which is referred to as a Dedekind-type DC-(Dahee and Changhee) sum. We establish analytic properties of this sum, find its trigonometric representations, and prove a reciprocity theorem for these sums. Furthermore, we obtain relationships between the Clausen functions, polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums, and the sum T p (h, k). We also give some applications related to these sums and functions.

Keywords

Zeta Function Euler Polynomial Euler Function Hurwitz Zeta Function Bernoulli Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Faculty of Arts and Science, Department of MathematicsAkdeniz UniversityAntalyaTurkey

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