A Study of Generalized Laguerre Poly-Genocchi Polynomials

A variety of polynomials, their extensions, and variants, have been extensively investigated, mainly due to their potential applications in diverse research areas. Motivated by their importance and potential for applications in a variety of research fields, numerous polynomials and their extensions have recently been introduced and investigated. In this paper, we introduce generalized Laguerre poly-Genocchi polynomials and investigate some of their properties and identities, which were found to extend some known results. Among them, an implicit summation formula and addition-symmetry identities for generalized Laguerre poly-Genocchi polynomials are derived. The results presented here, being very general, are pointed out to reduce to yield formulas and identities for relatively simple polynomials and numbers.