Abstract
In this paper, we consider the Barnes-type Peters polynomials. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.MSC:05A40, 11B83.
Highlights
The aim of this paper is to use umbral calculus to obtain several new and interesting identities of Barnes-type Peters polynomials
Umbral calculus has been used in numerous problems of mathematics
Umbral techniques have been used in different areas of physics; for example, it was used in group theory and quantum mechanics by Biedenharn et al [, ]
Summary
The aim of this paper is to use umbral calculus to obtain several new and interesting identities of Barnes-type Peters polynomials. Μr), which are called Barnes-type Peters polynomials of the first kind and of the second kind, respectively, and are given by r j=. ) are called Barnes-type Boole polynomials of the first kind and of the second kind. When x = , Sn = Sn(λ; μ) = Sn( |λ; μ) and Sn = Sn(λ; μ) = Sn( |λ; μ) are called Barnes-type Peters numbers of the first kind and of the second kind, respectively. Let be the algebra of polynomials in a single variable x over C, and let ∗ be the vector space of all linear functionals on.
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