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In this paper, a new form of poly-Genocchi polynomials is defined by means ofpoly-logarithm, namely, the Apostol-type poly-Genocchi polynomials of higherorder with parameters a, b and c. Several properties of these polynomials areestablished including some recurrence relations and explicit formulas, whichexpress these higher order Apostol-type poly-Genocchi polynomials in terms ofStirling numbers of the second kind, Apostol-type Bernoulli and Frobeniuspolynomials of higher order. Moreover, certain differential identity isobtained that leads this new form of poly-Genocchi polynomials to be classifiedas Appell polynomials and, consequently, draw more properties using sometheorems on Appell polynomials. Furthermore, a symmetrized generalization ofthis new form of poly-Genocchi polynomials is introduced that possesses adouble generating function. Finally, the type 2 Apostol-poly-Genocchipolynomials with parameters a, b and c are defined using the concept ofpolyexponential function and several identities are derived, two of which showthe connections of these polynomials with Stirling numbers of the first kindand the type 2 Apostol-type poly-Bernoulli polynomials.

Higher Order Apostol-Type Poly-Genocchi Polynomials with Parameters a, b and c