A Note on the Laguerre-Type Appell and Hypergeometric Polynomials

Abstract

The Laguerre derivative and its iterations have been used to define new sets of special functions, showing the possibility of generating a kind of parallel universe for mathematical entities of this kind. In this paper, we introduce the Laguerre-type Appell polynomials, in particular, the Bernoulli and Euler case, and we examine a set of hypergeometric Laguerre–Bernoulli polynomials. We show their main properties and indicate their possible extensions.

Keywords

• Laguerre-type exponentials
• Laguerre-type derivative
• Appell polynomials
• hypergeometric polynomials and numbers