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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.
- Arctangent sum
- Fibonacci number
- Lucas number
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Cite this paperAPA
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.