Abstract
In this paper, we introduce type 2 poly-Changhee polynomials by using the polyexponential function. We derive some explicit expressions and identities for these polynomials, and we also prove some relationships between poly-Changhee polynomials and Stirling numbers of the first and second kind. Also, we introduce the unipoly-Changhee polynomials by employing unipoly function and give multifarious properties. Furthermore, we provide a correlation between the unipoly-Changhee polynomials and the classical Changhee polynomials.
Highlights
Special polynomials and their generating functions have vital roles in several branches of arithmetic, probability, statistics, mathematical physics, and engineering
As an example, generating functions for special polynomials with their congruousness properties, repetition relations, process formulae, and regular add involving these polynomials are studied in recent years
We have touched on the problem of recognizing the algebraic structure underlying the polyChanghee polynomials as given by definition (16). e analysis is aimed at accounting for the wealth of the properties exhibited by these polynomials within the context of the poly-Changhee numbers and polynomials which provide a unifying formalism where the theory of special functions can be framed inherently
Summary
Special polynomials and their generating functions have vital roles in several branches of arithmetic, probability, statistics, mathematical physics, and engineering. For j ≥ 0, the Stirling numbers of the first kind are defined by the following (see [1, 2, 5,6,7,8,9,10,11,12,13,14]): j (ξ)j S1(j, l)ξl,. Journal of Mathematics e Bernoulli Bj(ξ), Euler Ej(ξ), and Genocchi Gj(ξ) polynomials are defined by the following (see [1, 6, 7]):. In 2019, Kim and Kim [12] introduced the poly-Bernoulli polynomials which are defined by. Letting ξ 0, B(jk) B(jk)(0) are called the poly-Bernoulli numbers. In the case when ξ 0, E(jk) E(jk)(0) are called the type 2 poly-Euler numbers.
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