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

In: Trigonometric Sums and Their Applications

Author

Listed:
  • Gradimir V. Milovanović

    (The Serbian Academy of Sciences and Arts
    University of Niš, Faculty of Sciences and Mathematics)

  • Yilmaz Simsek

    (Akdeniz University, Faculty of Arts and Science, Department of Mathematics)

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.

Suggested Citation

  • Gradimir V. Milovanović & Yilmaz Simsek, 2020. "Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas," Springer Books, in: Andrei Raigorodskii & Michael Th. Rassias (ed.), Trigonometric Sums and Their Applications, pages 183-228, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-37904-9_10
    DOI: 10.1007/978-3-030-37904-9_10
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