A short proof of a concrete sum

Samuel G. Moreno and Esther M. García-Caballero
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 23, 2017, Number 3, Pages 35–37
Full paper (PDF, 133 Kb)

Details

Authors and affiliations

Samuel G. Moreno
Departamento de Matematicas, Universidad de Jaén
23071 Jaen, Spain

Esther M. García-Caballero
Departamento de Matematicas, Universidad de Jaén
23071 Jaen, Spain

Abstract

We give an alternative proof of a formula that generalizes Hermite’s identity. Instead involving modular arithmetic, our short proof relies on the Fourier-type expansion for the floor function and on a trigonometric formula.

Keywords

  • Floor function
  • Fourier expansion
  • Trigonometric identity

AMS Classification

  • Primary: 11A99
  • Secondary: 42A10, 33B10

References

  1. Graham, R. L., Knuth, D. E., & Patashnik, O. (1994) Concrete Mathematics: A Foundation for Computer Science. Second edition. Addison-Wesley Publishing Co., Reading, Massachusetts.
  2. The Wolfram Functions Site, http://functions.wolfram.com/ ElementaryFunctions/Sin/23/01/0003/.

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Cite this paper

Moreno, S. G., & García-Caballero, E. M. (2017). A short proof of a concrete sum. Notes on Number Theory and Discrete Mathematics, 23(3), 35-37.

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