In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and t...In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and the relationship between special polynomials and numbers.Also,we introduce modified degenerate unipolyCauchy polynomials of the second kind and derive some fruitful properties of these polynomials.In addition,positive associated beautiful zeros and graphical representations are displayed with the help of Mathematica.展开更多
Recently,degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee.The aim of this paper is to further examine some properties of the degenerate poly-Bernou...Recently,degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee.The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed‘λ-umbral calculus.’In more detail,we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind,by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind,and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind.展开更多
基金supported by the Taif University Researchers Supporting Project(TURSP-2020/246),Taif University,Taif,Saudi Arabia.
文摘In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and the relationship between special polynomials and numbers.Also,we introduce modified degenerate unipolyCauchy polynomials of the second kind and derive some fruitful properties of these polynomials.In addition,positive associated beautiful zeros and graphical representations are displayed with the help of Mathematica.
文摘Recently,degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee.The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed‘λ-umbral calculus.’In more detail,we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind,by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind,and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind.
