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Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas

  • Gradimir V. Milovanović
  • Yilmaz Simsek
Chapter
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Abstract

The Dedekind and Hardy sums and several their generalizations, as well as the trigonometric sums obtained from the quadrature formulas with the highest (algebraic or trigonometric) degree of exactness are studied. Beside some typical trigonometric sums mentioned in the introductory section, the Lambert and Eisenstein series are introduced and some remarks and observations for Eisenstein series are given. Special attention is dedicated to Dedekind and Hardy sums, as well as to Dedekind type Daehee-Changhee (DC) sums and their trigonometric representations and connections with some special functions. Also, the reciprocity law of the previous mentioned sums is studied. Finally, the trigonometric sums obtained from Gauss-Chebyshev quadrature formulas, as well as ones obtained from the so-called trigonometric quadrature rules, are considered.

Keywords

Trigonometric sums Dedekind sums Hardy sums Eisenstein series Gauss-Chebyshev quadrature sums Degree of exactness 

Notes

Acknowledgements

The authors have been supported by the Serbian Academy of Sciences and Arts, Φ-96 (G. V. Milovanović) and by the Scientific Research Project Administration of Akdeniz University (Y. Simsek).

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Authors and Affiliations

  • Gradimir V. Milovanović
    • 1
    • 2
  • Yilmaz Simsek
    • 3
  1. 1.The Serbian Academy of Sciences and ArtsBelgradeSerbia
  2. 2.Faculty of Sciences and MathematicsUniversity of NišNišSerbia
  3. 3.Faculty of Arts and Science, Department of MathematicsAkdeniz UniversityAntalyaTurkey

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