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

  • Y. Simsek


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.


Zeta Function Euler Polynomial Euler Function Hurwitz Zeta Function Bernoulli Function 
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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

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

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