Some Properties of Generalized Apostol-Type Frobenius-Euler-Fibonacci Polynomials
Maryam Salem Alatawi, Waseem Ahmad Khan, Can Kizilates, Cheon Seoung Ryoo
article (Uluslararası, Hakemli) | Yazar(lar): Maryam Salem Alatawi, Waseem Ahmad Khan, Can Kizilates, Cheon Seoung Ryoo | Yıl: 2024 | Dergi/Kurum: MATHEMATICS | İndeks: WOS.SCI | DOI: 10.3390/math12060800 | Anahtar Kelimeler: Golden Calculus, Apostol-type Frobenius-Euler polynomials, Apostol-type Frobenius-Euler-Fibona
In this paper, by using the Golden Calculus, we introduce the generalized Apostol-type Frobenius-Euler-Fibonacci polynomials and numbers; additionally, we obtain various fundamental identities and properties associated with these polynomials and numbers, such as summation theorems, difference equations, derivative properties, recurrence relations, and more. Subsequently, we present summation formulas, Stirling-Fibonacci numbers of the second kind, and relationships for these polynomials and numbers. Finally, we define the new family of the generalized Apostol-type Frobenius-Euler-Fibonacci matrix and obtain some factorizations of this newly established matrix. Using Mathematica, the computational formulae and graphical representation for the mentioned polynomials are obtained.