Special functions related to Dedekind-type DC-sums and their applications
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, vol.17, no.4, pp.495-508, 2010 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 17 Issue: 4
- Publication Date: 2010
- Doi Number: 10.1134/s1061920810040114
- Journal Name: RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.495-508
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
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.