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On hyper (r, q)-Fibonacci polynomials

  • Hacéne Belbachir EMAIL logo and Fariza Krim
Published/Copyright: May 13, 2024
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Abstract

Related to generalized arithmetic triangle, we introduce the hyper (r, q)-Fibonacci polynomials as the sum of these elements along a finite ray starting from a specific point, which generalize the hyper-Fibonacci polynomials. We give generating function, recurrence relations and we show some properties whose application allows us to extend the notion of Cassini determinant and to study some ratios. Moreover, we derive a connection between these polynomials and the incomplete (r, q)-Fibonacci polynomials defined in this paper.


This work is partially supported by DGRSDT Grant no 0656701.




  1. (Communicated by István Gaál)

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Received: 2022-08-18
Accepted: 2023-03-26
Published Online: 2024-05-13
Published in Print: 2024-02-26

© 2024 Mathematical Institute Slovak Academy of Sciences

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