On Certain Properties of Parametric Kinds of Apostol-Type Frobenius-Euler-Fibonacci Polynomials
Hao Guan, Waseem Ahmad Khan, Can Kizilates, Cheon Seoung Ryoo
article (Uluslararası, Hakemli) | Yazar(lar): Hao Guan, Waseem Ahmad Khan, Can Kizilates, Cheon Seoung Ryoo | Yıl: 2024 | Dergi/Kurum: AXIOMS | İndeks: WOS.SCI | DOI: 10.3390/axioms13060348 | Anahtar Kelimeler: Golden calculus, cosine-Apostol-type Frobenius-Euler-Fibonacci polynomials, sine-Apostol-type Frobenius Euler
This paper presents an overview of cosine and sine Apostol-type Frobenius-Euler-Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating functions, the authors obtain derivative formulae and finite combinatorial sums involving these polynomials and numbers. Additionally, the paper establishes connections between cosine and sine Apostol-type Frobenius-Euler-Fibonacci polynomials of order alpha and several other polynomial sequences, such as the Apostol-type Bernoulli-Fibonacci polynomials, the Apostol-type Euler-Fibonacci polynomials, the Apostol-type Genocchi-Fibonacci polynomials, and the Stirling-Fibonacci numbers of the second kind. The authors also provide computational formulae and graphical representations of these polynomials using the Mathematica program.