On Multi Poly-Genocchi Polynomials with Parameters a, b and c

Abstract

Most identities of Genocchi numbers and polynomials are related to the well-knownBenoulli and Euler polynomials. In this paper, multi poly-Genocchi polynomials withparameters a, b and c are dened by means of multiple parameters polylogarithm. Several properties of these polynomials are established including some recurrence relations and explicit formulas.

Degenerate Apostol-Frobenius Type Poly-Genocchi Polynomials of Higher Order with Parameters a and b

“…n are called the poly-Genocchi numbers. It is worth-mentioning that, using multi-polylogarithm, the generalized poly-Genocchi polynomials in ( 9) and ( 10) have been extended further in [39]. Recently, a new variation of poly-Genocchi polynomials with parameters a, b and c was defined in [17] by mixing the definitions of polylogarithm, Apostol-Genocchi polynomials and Frobenius polynomials, namely, the Apostol-Frobenius-type poly-Genocchi polynomials of higher order with parameters a, b and c. More precisely, the said polynomials, denoted by G (k,α) n (x; λ, ρ, u, a, b), are defined as coefficients of the following generating function…”