The Ramanujan Journal

, Volume 50, Issue 3, pp 621–637 | Cite as

Infinite sums for Fibonacci polynomials and Lucas polynomials

  • Bing HeEmail author
  • Ruiming Zhang


In this paper we establish certain infinite sums involving many arithmetical functions and the Fibonacci polynomials or the Lucas polynomials. Several of the sums are given explicitly in Jacobi theta functions.


Infinite reciprocal sum Fibonacci polynomials Lucas polynomials Arithmetical function 

Mathematics Subject Classification

11B39 11F27 



The authors would like to thank the referee for his/her helpful comments.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of ScienceNorthwest A&F UniversityYanglingPeople’s Republic of China

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