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On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

Author

Listed:
  • Can Kızılateş

    (Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan)

  • Nazlıhan Terzioğlu

    (Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey)

Abstract

This paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics. In this paper, by using higher-order generalized Fibonacci polynomials, we introduce higher-order generalized Fibonacci hybrid polynomials called higher-order generalized Fibonacci hybrinomials. We obtain some special cases and algebraic properties of the higher-order generalized Fibonacci hybrinomials, such as the recurrence relation, generating function, exponential generating function, Binet formula, Vajda’s identity, Catalan’s identity, Cassini’s identity and d’Ocagne’s identity. We also present three different matrices whose components are higher-order generalized Fibonacci hybrinomials, higher-order generalized Fibonacci polynomials and Lucas polynomials. By using these matrices, we obtain some identities related to these newly established hybrinomials.

Suggested Citation

  • Can Kızılateş & Wei-Shih Du & Nazlıhan Terzioğlu, 2024. "On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations," Mathematics, MDPI, vol. 12(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1156-:d:1374252
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    References listed on IDEAS

    as
    1. E. Gokcen Kocer & Huriye Alsan, 2022. "Generalized Hybrid Fibonacci and Lucas p-numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 948-955, December.
    2. Can Kızılateş & Tiekoro Kone, 2023. "On special spacelike hybrid numbers with Fibonacci divisor number components," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(1), pages 279-287, March.
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