Abstract
In this paper, we introduce the mixed-type polynomials: Barnes-type Daehee polynomials of the second kind and poly-Cauchy polynomials of the second kind. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities. MSC:05A19, 05A40, 11B68, 11B75.
Highlights
1 Introduction In this paper, we consider the polynomials D(nk)(x|a, . . . , ar) called the Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials, whose generating function is given by r ln( + t)( + t)aj ( + t)aj
We introduce the mixed-type polynomials: Barnes-type Daehee polynomials of the second kind and poly-Cauchy polynomials of the second kind
From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities
Summary
We consider the polynomials D(nk)(x|a , . . . , ar) called the Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials, whose generating function is given by r ln( + t)( + t)aj ( + t)aj – Lifk. Ar) called the Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials, whose generating function is given by r ln( + t)( + t)aj ( + t)aj – Lifk. Recall that the Barnes-type Daehee polynomials of the second kind, denoted by Dn(x|a , . The poly-Cauchy polynomials of the second kind, denoted by c(nk)(x) [ , ], are given by the generating function as follows: c(nk). L|p(x) is the action of the linear functional L on the polynomial p(x), and we recall that the vector space operations on P∗ are defined by L + M|p(x) = L|p(x) + M|p(x) , cL|p(x) = c L|p(x) , where c is a complex constant in C. Sheffer sequences are characterized in the generating function [ , Theorem .
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