Abstract
In this paper, we consider Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.
Highlights
In this paper, we consider the polynomials Tn(r,k)(x|a, . . . , ar; λ, . . . , λr) whose generating function is given by r j= – λj eajt – λjLik( – e–t) – e–t ext = ∞ Tn(r,k)
1 Introduction In this paper, we consider the polynomials Tn(r,k)(x|a, . . . , ar; λ, . . . , λr) whose generating function is given by r j=
From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities
Summary
We consider the polynomials Tn(r,k)(x|a , . . . , ar; λ , . . . , λr) whose generating function is given by r j=. Λr) will be called Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials. Λr) will be called Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type numbers. For every integer k, the poly-Bernoulli polynomials B(nk)(x) are defined by the generating function as follows: ext. Λr) are defined by the generating function as follows:. Note that the Frobenius-Euler polynomials of order r, Hn(r)(x|λ) are defined by the generating function. We consider Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixedtype polynomials. 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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