A Study of Generalized Laguerre Poly-Genocchi Polynomials

Abstract

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.

Construction of the type 2 poly-Frobenius–Genocchi polynomials with their certain applications

“…Motivated and inspired by the definition of the unipoly-Bernoulli polynomials in (10) given by Kim and Kim [12], we introduce unipoly-Frobenius-Genocchi polynomials by means of the unipoly function attached to p given in (9) as follows:…”