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The \({h(x)}\)-Fibonacci Quaternion Polynomials: Some Combinatorial Properties

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Abstract

In this paper we consider the \({h(x)}\)-Fibonacci quaternion polynomials and present some properties involving these polynomials, including the exponential and Poisson generating functions.

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References

  1. Akyigit M., Kösal H.H., Tosun M.: Fibonacci generalized quaternions. Adv. Appl. Clifford Algebras 24(3), 631–641 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bolat C., Köse H.: On the properties of k-Fibonacci numbers. Int. J. Contemp. Math. Sci. 22(5), 1097–1105 (2010)

    MathSciNet  MATH  Google Scholar 

  3. Catarino P.: On some identities for k-Fibonacci sequence. Int. J. Contemp. Math. Sci. 9(1), 37–42 (2014)

    Google Scholar 

  4. Catarino P.: A note on \({h(x)}\)-Fibonacci quaternion polynomials. Chaos Solitons Fractals 77, 1–5 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  5. Catarino, P., Vasco, P., Borges, A., Campos, H., Aires, A.P.: Sums, products and identities involving k-Fibonacci and k-Lucas sequences. JP J. Algebra Number Theory Appl. 32(1), 63–77 (2014)

  6. Conway, J.H., Smith, D.A.: On Quaternions and Octonions: Their Geometry, Arithmetic and Symmetry. A. K. Peters, Natick (2003)

  7. Falcón S., Plaza A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos Solitons Fractals 33, 38–49 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  8. Flaut C., Shpakivskyi V.: On generalized Fibonacci quaternions and Fibonacci–Narayana quaternions. Adv. Appl. Clifford Algebras 23(3), 673–688 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Halici S.: On Fibonacci quaternions. Adv. Appl. Clifford Algebras 22(2), 321–327 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hoggatt, V.E.: Fibonacci and Lucas Numbers. A Publication of the Fibonacci Association. University of Santa Clara, Santa Clara. Houghton Mifflin Company, Boston (1969)

  11. Horadam A.F.: Complex Fibonacci numbers and Fibonacci quaternions. Am. Math. Mon. 70, 289–291 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  12. Horadam A.F.: Recurrence relations. Ulam Q. 2(2), 23–33 (1993)

    MathSciNet  MATH  Google Scholar 

  13. Iyer M.R.: Some results on Fibonacci quaternions. Fibonacci Q. 7(2), 201–210 (1969)

    MathSciNet  MATH  Google Scholar 

  14. Iyer M.R.: Note on Fibonacci quaternions. Fibonacci Q. 7(3), 225–229 (1969)

    MathSciNet  MATH  Google Scholar 

  15. Koshy, T.: Fibonacci and Lucas Numbers with Applications. Wiley, New York (2001)

  16. Larcombe P., Bagdasar O., Fennessey E.: Horadam sequences: a survey. Bull. Inst. Comb. Appl. 67, 49–72 (2013)

    MathSciNet  MATH  Google Scholar 

  17. Nalli A., Haukkanen P.: On generalized Fibonacci and Lucas polynomials. Chaos Solitons Fractals 42, 3179–3186 (2009)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  18. Ramírez J.: Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions. An. St. Univ. Ovidius Constanta 23(2), 201–212 (2015)

    MathSciNet  Google Scholar 

  19. Swamy M.N.: On generalized Fibonacci quaternions. Fibonacci Q. 11(5), 547–549 (1973)

    MathSciNet  MATH  Google Scholar 

  20. Vorobiov, N.N.: Lecciones populares de matemáticas: NUMEROS DE FIBONACCI. Editorial MIR, Moscú, URSS (1974)

  21. Ward, J.P.: Quaternions and Cayley Numbers: Algebra and Applications. Kluwer, Dordrecht (1997)

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Correspondence to Paula Catarino.

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Catarino, P. The \({h(x)}\)-Fibonacci Quaternion Polynomials: Some Combinatorial Properties. Adv. Appl. Clifford Algebras 26, 71–79 (2016). https://doi.org/10.1007/s00006-015-0606-1

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  • DOI: https://doi.org/10.1007/s00006-015-0606-1

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