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AIMS Mathematics

2022, Volume 7, Issue 7: 12962-12980. doi: 10.3934/math.2022718
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Research article

Some new identities of a type of generalized numbers involving four parameters

  • 1.
    Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
  • 2.
    Department of Basic Sciences, Adham University College, Umm AL-Qura University, Saudi Arabia
  • 3.
    Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
  • 4.
    Department of Mathematics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
  • Received: 16 March 2022 Revised: 25 April 2022 Accepted: 26 April 2022 Published: 07 May 2022

  • MSC : 11B39, 11B83

  • This article deals with a Horadam type of generalized numbers involving four parameters. These numbers generalize several celebrated numbers in the literature such as the generalized Fibonacci, generalized Lucas, Fibonacci, Lucas, Pell, Pell-Lucas, Fermat, Fermat-Lucas, Jacobsthal, Jacobsthal-Lucas, balancing, and co-balancing numbers. We present some new identities concerned with the generalized numbers of four parameters. An explicit expression for these numbers is developed, and a mixed recurrence relation between two certain families of the generalized numbers is given, and after that, some new identities are presented and proved. A large number of identities between several celebrated numbers are obtained as special cases of our developed ones. Furthermore, some of the identities that were previously published in other articles can be deduced as special ones of our new identities.

    Citation: Waleed Mohamed Abd-Elhameed, Amr Kamel Amin, Nasr Anwer Zeyada. Some new identities of a type of generalized numbers involving four parameters[J]. AIMS Mathematics, 2022, 7(7): 12962-12980. doi: 10.3934/math.2022718

    Related Papers:

  • This article deals with a Horadam type of generalized numbers involving four parameters. These numbers generalize several celebrated numbers in the literature such as the generalized Fibonacci, generalized Lucas, Fibonacci, Lucas, Pell, Pell-Lucas, Fermat, Fermat-Lucas, Jacobsthal, Jacobsthal-Lucas, balancing, and co-balancing numbers. We present some new identities concerned with the generalized numbers of four parameters. An explicit expression for these numbers is developed, and a mixed recurrence relation between two certain families of the generalized numbers is given, and after that, some new identities are presented and proved. A large number of identities between several celebrated numbers are obtained as special cases of our developed ones. Furthermore, some of the identities that were previously published in other articles can be deduced as special ones of our new identities.


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