Further results on arctangent sums with applications to generalized Fibonacci numbers

Robert Frontczak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 1, Pages 39—53
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Authors and affiliations

Robert Frontczak
Landesbank Baden-Wuerttemberg
Am Hauptbahnhof 2, 70173 Stuttgart, Germany

Abstract

In this article, we extend a classical trigonometric addition formula for the arctangent function and derive new summation identities for Fibonacci and Lucas numbers. While most of the results seem to be new, we also recover some known expressions.

Keywords

  • Arctangent sum
  • Fibonacci number
  • Lucas number

AMS Classification

  • 11B37
  • 11B39

References

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Cite this paper

APA

Frontczak, R. (2017). Further results on arctangent sums with applications to generalized Fibonacci numbers. Notes on Number Theory and Discrete Mathematics, 23(1), 39-53.

Chicago

Frontczak, Robert. “Further Results on Arctangent Sums with Applications to Generalized Fibonacci Numbers.” Notes on Number Theory and Discrete Mathematics 23, no. 1 (2017): 39-53.

MLA

Frontczak, Robert. ”Further Results on Arctangent Sums with Applications to Generalized Fibonacci Numbers.” Notes on Number Theory and Discrete Mathematics 23.1 (2017): 39-53. Print.

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