Infinite arctangent sums involving Fibonacci and Lucas numbers

Kunle Adegoke
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 1, Pages 56—66
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Authors and affiliations

Kunle Adegoke
Department of Physics, Obafemi Awolowo University
Ile-Ife, 220005 Nigeria

Abstract

We derive numerous infinite arctangent summation formulas involving Fibonacci and Lucas numbers. While most of the results obtained are new, a couple of ‘celebrated’ results appear as particular cases of the more general formulas derived here.

Keywords

  • Fibonacci numbers
  • Lucas numbers
  • Lehmer’s formula
  • Arctangent sums
  • Infinite sums

AMS Classification

  • 11B39
  • 11Y60

References

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  4. Mahon, J. M., Br., & Horadam, A. F. (1985) Inverse trigonometrical summation formulas involving Pell polynomials. The Fibonacci Quarterly, 23(4), 319–324.
  5. Melham, R. S. & Shannon, A. G. (1995) Inverse trigonometric and hyperbolic summation formulas involving generalized Fibonacci numbers. The Fibonacci Quarterly, 33(1),32–40.
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  7. Dunlap, R. A. (2003) The Golden Ratio and Fibonacci Numbers. World Scientific.
  8. Howard, F. T. (2003) The sum of the squares of two generalized Fibonacci numbers. The Fibonacci Quarterly, 41(1), 80–84.

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Cite this paper

APA

Adegoke, K. (2015). Infinite arctangent sums involving Fibonacci and Lucas numbers. Notes on Number Theory and Discrete Mathematics, 21(1), 56-66.

Chicago

Adegoke, Kunle. “Infinite Arctangent Sums Involving Fibonacci and Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 56-66.

MLA

Adegoke, Kunle. “Infinite Arctangent Sums Involving Fibonacci and Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 56-66. Print.

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