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

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Simsek Y.

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, cilt.17, sa.4, ss.495-508, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 4
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1134/s1061920810040114
  • Dergi Adı: RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.495-508
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.