The Ramanujan Journal

, Volume 49, Issue 1, pp 1–37 | Cite as

On exponential and trigonometric functions on nonuniform lattices

  • M. Kenfack Nangho
  • M. Foupouagnigni
  • W. KoepfEmail author


We develop analogs of exponential and trigonometric functions (including the basic exponential function) and derive their fundamental properties: addition formula, positivity, reciprocal and fundamental relations of trigonometry. We also establish a binomial theorem, characterize symmetric orthogonal polynomials and provide a formula for computing the nth-derivatives for analytic functions on nonuniform lattices (q-quadratic and quadratic variables).


Basic exponential function Askey–Wilson polynomials Symmetric functions and nonuniform lattices 

Mathematics Subject Classification

33D15 39D45 



The authors thank the anonymous referees for their fruitful comments and careful checking of proofs that resulted in an improvement of our paper.


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Copyright information

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Authors and Affiliations

  • M. Kenfack Nangho
    • 1
    • 2
  • M. Foupouagnigni
    • 3
    • 4
  • W. Koepf
    • 5
    Email author
  1. 1.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa
  2. 2.Department of Mathematics and Computer Science, Faculty of ScienceUniversity of DschangDschangCameroon
  3. 3.Department of Mathematics, Higher Teachers’ Training CollegeUniversity of Yaounde IYaoundéCameroon
  4. 4.African Institute for Mathematical SciencesLimbéCameroon
  5. 5.Institute of MathematicsUniversity of KasselKasselGermany

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