The Journal of the Indian Mathematical Society

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On a Generalization of Incomplete Fibonacci Quaternions


Affiliations
1 Department of Mathematics, School of Applied Sciences KIIT, University, Bhubaneswar-751024, India
2 Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-751024, India
     

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The aim of this article is to introduce a new class of quater- nions, namely, incomplete Horadam quaternions that are based on in- complete Horadam numbers which generalize the previously introduced incomplete Fibonacci and Lucas quaternions. Further, some identities including summation formulas and generating functions concerning these quaternions are also established.

Keywords

Quaternion, Horadam numbers, Incomplete Horadam numbers, Incomplete Fibonacci quaternions
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  • J. Baez, The octonions, Bull. Amer. Math. Soc., 39. (2002), 145-205.

  • H. Belbachir and A. Belkhir, On some generalizations of Horadams numbers, Filomat, 32. (2018), 5037-5052.

  • P. Catarino and H. Campos, Incomplete k-Pell, k-Pell-Lucas and modi ed k-Pell num- bers, Hacet. J. Math. Stat., 46. (2017), 361-372.

  • G. B. Djordjevic and H. M. Srivastava, Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers, Math. Comput. Modelling, 42. (2005), 9-10.

  • T. A. Ell, N. L. Bihan and S. J. Sangwine, Quaternion Fourier transforms for signal and image processing. John Wiley & Sons: 2014.

  • P. Filipponi, Incomplete Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo., 45. (2) (1996), 37-56.

  • S. Halici and A. Karatas, On a generalization for Fibonacci quaternions, Chaos Solitons Fractals, 98. (2017), 178-182.

  • A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly, 70. (1963), 289-291.

  • C. Kzlates, On quaternions with incomplete Fibonacci and Lucas numbers components, Util. Math., 110. (2019), 263-269.

  • K. I. Kou and Y. H. Xia, Linear quaternion di erential equations: Basic theory and fundamental results, Stud. Appl. Math., 141. (2018), 3-45.

  • B. K. Patel, N. Irmak and P. K. Ray, Incomplete balancing and Lucas-balancing numbers, Math. Rep. (Bucur.), 20. (2018), 59-72.

  • A. Pinter and H. M. Srivastava, Generating functions of the incomplete Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo, 48. (2) (1999), 591-596.

  • H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions. Halsted Press, Ellis Horwood Limited, Chichester, UK, John Wiley & Sons: 1984.

  • M. Startek, A. W loch and I. W loch, Fibonacci numbers and Lucas numbers in graphs, Discrete Appl. Math., 157. (2009), 864-868.

  • D. Tasci and M. C. Firengiz, Incomplete Fibonacci and Lucas p-numbers, Math. Comput. Modelling, 52. (2010), 1763-1770.


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  • On a Generalization of Incomplete Fibonacci Quaternions

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Authors

Bijan Kumar Patel
Department of Mathematics, School of Applied Sciences KIIT, University, Bhubaneswar-751024, India
Narmada Behera
Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar-751024, India

Abstract


The aim of this article is to introduce a new class of quater- nions, namely, incomplete Horadam quaternions that are based on in- complete Horadam numbers which generalize the previously introduced incomplete Fibonacci and Lucas quaternions. Further, some identities including summation formulas and generating functions concerning these quaternions are also established.

Keywords


Quaternion, Horadam numbers, Incomplete Horadam numbers, Incomplete Fibonacci quaternions

References





DOI: https://doi.org/10.18311/jims%2F2021%2F25549