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
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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

APA

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.

Chicago

Moreno, Samuel G., and Esther M. García-Caballero. “A short proof of a concrete sum.” Notes on Number Theory and Discrete Mathematics 23, no. 3 (2017): 35-37.

MLA

Moreno, Samuel G., and Esther M. García-Caballero. “A short proof of a concrete sum.” Notes on Number Theory and Discrete Mathematics 23.3 (2017): 35-37. Print.

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