Some Properties of Generalized Apostol-Type Frobenius–Euler–Fibonacci Polynomials

Maryam Salem Alatawi, Waseem Ahmad Khan (), Can Kızılateş and Cheon Seoung Ryoo
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Maryam Salem Alatawi: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Waseem Ahmad Khan: Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia
Can Kızılateş: Department of Mathematics, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey
Cheon Seoung Ryoo: Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea

Mathematics, 2024, vol. 12, issue 6, 1-15

Abstract: 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.

Keywords: Golden Calculus; Apostol-type Frobenius–Euler polynomials; Apostol-type Frobenius–Euler–Fibonacci polynomials; Stirling–Fibonacci numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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