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RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, vol.17, no.4, pp.495-508, 2010 (SCI-Expanded)
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.