??-Laguerre based Appell polynomials and their properties associated with some special polynomials

Abstract

In the present paper, we introduce ?(?)-Laguerre based Appell polynomials. The first main aim of the paper is to investigate their main properties including explicit representa-tion, determinantal form, recurrence relation, lowering operators ( LO ) , integro-partial rais-ing operator (IPRO) and integro-partial difference equation (IPDE). The second aim is to give the corresponding results, which are known or new, to the usual Laguerre based Appell polynomials which can be obtain immediately from the limiting case ? ? 0 . Furthermore, we introduce ?(?)-Laguerre-Carlitz Bernoulli, ?(?)-Laguerre-Carlitz Euler, ?(?)- Laguerre-Miller-Lee, ?(?)-Laguerre-Boole polynomials and ?(?)-Laguerre-Bernoulli polyno-mials of the second kind as particular cases of ?(?)-Laguerre based Appell polynomials. The corresponding main results have also been exhibited for these new families of poly-nomials.