2009/02/02 by Y. Simsek, Yilmaz Simsek
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Polylogarithm #Proofs of trigonometric identities #Reciprocity (cultural anthropology) #Trigonometric functions #Trigonometric polynomial #Trigonometric series #Trigonometric substitution #Trigonometry #math.CV #math.NT #msc:11B68 #msc:11F20 #msc:11M35 #msc:11M41 #msc:11S80 #msc:33C10 #msc:33E20
paper · pdf · doi:10.1134/s1061920810040114
published as Russian Journal of Mathematical Physics 2010
arxiv created 2009/02/02 · openalex publication_date 2010/12/01 · openalex created_date 2016/06/24 · arxiv updated 2018/11/19 · openalex updated_date 2026/08/05
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.