Two-Variable Type 2 Poly-Fubini Polynomials

Abstract

In the present work, a new extension of the two-variable Fubini polynomials is introduced by means of the polyexponential function, which is called the two-variable type 2 poly-Fubini polynomials. Then, some useful relations including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoulli polynomials are derived. Also, some summation formulas and an integral representation for type 2 poly-Fubini polynomials are investigated. Moreover, two-variable unipoly-Fubini polynomials are introduced utilizing the unipoly function, and diverse properties involving integral and derivative properties are attained. Furthermore, some relationships covering the two-variable unipoly-Fubini polynomials, the Stirling numbers of the second and the first kinds, and the Daehee polynomials are acquired.

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.…”

Some Identities of the Degenerate Multi-Poly-Bernoulli Polynomials of Complex Variable

“…In Section 3, we consider the degenerate multi-poly-Bernoulli polynomials of a complex variable and then we derive several properties and relations. Also, we examine the results derived in this study [28,29].…”

A Note on Type-Two Degenerate Poly-Changhee Polynomials of the Second Kind

“…(see [6,[13][14][15][16][17][18][19]). Note here that lim λ→0 S 1,λ (n, k) = S 1 (n, k), where S 1 (n, k) are the Stirling numbers of the first kind given by…”