The Appell-Fibonacci Polynomials

Kuş S., DUMAN E., TUĞLU N.

8th International conference Approximation Theory and Special Functions, ATSF 2024, Ankara, Türkiye, 4 - 07 Eylül 2024, cilt.503 PROMS, ss.393-409, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 503 PROMS
  • Doi Numarası: 10.1007/978-3-031-93279-3_21
  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.393-409
  • Anahtar Kelimeler: Appell polynomial, Recurrence relation
  • Gazi Üniversitesi Adresli: Evet

Özet

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.