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Trigonometric Sums and Their Applications pp 183–228Cite as

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

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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.

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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

  1. The Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  2. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

    Gradimir V. Milovanović

  3. Faculty of Arts and Science, Department of Mathematics, Akdeniz University, Antalya, Turkey

    Yilmaz Simsek

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  1. Gradimir V. Milovanović
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Editors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Moscow state University, Moscow, Russia, Buryat State University, Ulan-Ude, Russia, Caucasus Mathematical Center, Adyghe State University, Maykop, Russia

    Andrei Raigorodskii

  2. Institute of Mathematics, University of Zurich, Zurich, Switzerland, Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Institute for Advanced Study Program in Interdisciplinary Studies, Princeton, NJ, USA

    Michael Th. Rassias

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Milovanović, G.V., Simsek, Y. (2020). Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas. In: Raigorodskii, A., Rassias, M. (eds) Trigonometric Sums and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-37904-9_10

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