Construction on the Degenerate Poly-Frobenius-Euler Polynomials of Complex Variable

Abstract

In this paper, we introduce degenerate poly-Frobenius-Euler polynomials and derive some identities of these polynomials. We give some relationships between degenerate poly-Frobenius-Euler polynomials and degenerate Whitney numbers and Stirling numbers of the first kind. Moreover, we define degenerate poly-Frobenius-Euler polynomials of complex variables and then we derive several properties and relations.

A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

“…Some of the most significant polynomials in the theory of special polynomials are the Bell, Euler, Bernoulli, Hermite, and Genocchi polynomials. Recently, the aforesaid polynomials and their diverse generalizations have been densely considered and investigated by many physicists and mathematicians (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]22]) and see also the references cited therein (see [6][7][8][9][14][15][16][17]). The class of Appell polynomial sequence is one of the significant classes of polynomials sequence [1].…”

“…Motivated by the importance and potential applications in certain problems in number theory, combinatorics, classical and numerical analysis and physics, several families of Bernoulli and Euler polynomials and special polynomials have been recently studied by many authors, see [8,9,[19][20][21]. Recently, Kim et al [13,16] have introduced the degenerate Bernoulli and degenerate Euler polynomials of a complex variable.…”

Applications and Properties for Bivariate Bell-Based Frobenius-Type Eulerian Polynomials

“…In recent times, the use of sine and cosine polynomials has led to the definition and construction of generating functions for new families of special polynomials, such as Bernoulli, Euler, and Genocchi; see [1][2][3][4]. Fundamental properties and diverse applications for these polynomials have been provided by these types of studies.…”

“…In addition, they investigated many relations for the polynomials given above. The trigonometric polynomials, cosine, and sine polynomials are introduced as follows (see [2][3][4]7]):…”

Some Identities of the Degenerate Poly-Cauchy and Unipoly Cauchy Polynomials of the Second Kind

“…Recently, many mathematicians, specifically Carlitz [1,2], Kim et al [3][4][5], Kim et al [6,7], Sharma et al [8,9], Khan et al [10][11][12][13], and Muhiuddin et al [14][15][16][17] have studied and added diverse degenerate versions of many special polynomials and numbers (like as degenerate Bernoulli polynomials, degenerate Euler polynomials, degenerate Daehee polynomials, degenerate Fubini polynomials, degenerate Stirling numbers of the first and second kind, and so on). In this paper, we focus on modified degenerate polyexponential Cauchy (or poly-Cauchy) polynomials and the numbers of the second type.…”