Some new identities of a type of generalized numbers involving four parameters
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,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022718?viewType=HTML |
| _version_ | 1811335688280342528 |
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| author | Waleed Mohamed Abd-Elhameed Amr Kamel Amin Nasr Anwer Zeyada |
| author_facet | Waleed Mohamed Abd-Elhameed Amr Kamel Amin Nasr Anwer Zeyada |
| author_sort | Waleed Mohamed Abd-Elhameed |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T17:27:58Z |
| format | Article |
| id | doaj.art-87c49577ff684bdeb69204f266fa1f4d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T17:27:58Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-87c49577ff684bdeb69204f266fa1f4d2022-12-22T02:37:41ZengAIMS PressAIMS Mathematics2473-69882022-05-0177129621298010.3934/math.2022718Some new identities of a type of generalized numbers involving four parametersWaleed Mohamed Abd-Elhameed0Amr Kamel Amin1Nasr Anwer Zeyada21. Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt2. 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, Egypt1. Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt4. Department of Mathematics, College of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaThis 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.https://www.aimspress.com/article/doi/10.3934/math.2022718?viewType=HTMLgeneralized fibonacci and generalized lucas numberslucas and fibonacci numbersrecurrence relationzeilberger's algorithm |
| spellingShingle | Waleed Mohamed Abd-Elhameed Amr Kamel Amin Nasr Anwer Zeyada Some new identities of a type of generalized numbers involving four parameters AIMS Mathematics generalized fibonacci and generalized lucas numbers lucas and fibonacci numbers recurrence relation zeilberger's algorithm |
| title | Some new identities of a type of generalized numbers involving four parameters |
| title_full | Some new identities of a type of generalized numbers involving four parameters |
| title_fullStr | Some new identities of a type of generalized numbers involving four parameters |
| title_full_unstemmed | Some new identities of a type of generalized numbers involving four parameters |
| title_short | Some new identities of a type of generalized numbers involving four parameters |
| title_sort | some new identities of a type of generalized numbers involving four parameters |
| topic | generalized fibonacci and generalized lucas numbers lucas and fibonacci numbers recurrence relation zeilberger's algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022718?viewType=HTML |
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