On Appell-Laguerre polynomials

Abstract

In this note we give a digest study of Appell-Laguerre polynomials, we provide a recurrence relation and a second-order differential equation satisfied by these polynomials. Moreover, an explicit expression and a generating function of the polynomials are given. The location and the number of the real zeros of Appell-Laguerre polynomials are determined; consequently, we recover information about the zeros of Laguerre polynomials when the range of the parameter α is the whole real axis excepting the negative integers.