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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1821–1829 | Cite as

A Determinantal Expression for the Fibonacci Polynomials in Terms of a Tridiagonal Determinant

  • Feng Qi
  • Jing-Lin Wang
  • Bai-Ni GuoEmail author
Original Paper

Abstract

In the paper, after concisely reviewing and surveying some known results, the authors find a determinantal expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

Keywords

Determinantal expression Fibonacci number Fibonacci polynomial Tridiagonal determinant Hessenberg determinant 

Mathematics Subject Classification

11B39 11B83 11C20 11Y55 15A15 65F40 

Notes

Acknowledgements

The authors express many thanks to anonymous referees for their careful corrections to and valuable comments on the original version of this paper.

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.College of MathematicsInner Mongolia University for NationalitiesTongliaoChina
  2. 2.School of Mathematics and InformaticsHenan Polytechnic UniversityJiaozuoChina
  3. 3.Teda No. 2 Primary School, No. 98, The Fifth StreetEconomic and Technological Development ZoneTianjinChina
  4. 4.School of Mathematical SciencesTianjin Polytechnic UniversityTianjinChina

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