The Appell-Fibonacci Polynomials

Kuş S., DUMAN E., TUĞLU N.

8th International conference Approximation Theory and Special Functions, ATSF 2024, Ankara, Turkey, 4 - 07 September 2024, vol.503 PROMS, pp.393-409, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 503 PROMS
  • Doi Number: 10.1007/978-3-031-93279-3_21
  • City: Ankara
  • Country: Turkey
  • Page Numbers: pp.393-409
  • Keywords: Appell polynomial, Recurrence relation
  • Gazi University Affiliated: Yes

Abstract

The main purpose of this paper is to define the Appell-Fibonacci polynomials by associating the Appell polynomials, an important concept in mathematics, with Fibonomial coefficients. In this study, various properties and recurrence relations of the Appell-Fibonacci polynomials were established, and a determinantal definition is provided. Additionally, the Appell-Fibonacci polynomial matrix is defined, and its relationship with the generalized Fibo-Pascal matrix is presented. Lastly, the generating function for Appell-Fibonacci polynomials is extended to bilinear and bilateral functions and showcasing several special results.