On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus
Can Kizilates, Halit Ozturk
article (Uluslararası, Hakemli) | Yazar(lar): Can Kizilates, Halit Ozturk | Yıl: 2023 | Dergi/Kurum: AIMS MATHEMATICS — Özet: This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol
This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol Genocchi-Fibonacci polynomials by using Golden calculus. Numerous properties of these polynomials with their generating functions are investigated. These generating functions give us a generalization of some well-known generating functions for special polynomials such as Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials. Using the Golden differential operator technique, the functional equation method for generating function, we present some properties of these newly established polynomials.