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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## Details

### 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

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## Cite this paper

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

ChicagoFrontczak, 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.

MLAFrontczak, 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.