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

Abstract

This paper introduces another variation of poly-Genocchi polynomials by mixing the concept of modified degenerate polyexponential function, Apostol-Genocchi polynomials and Frobenius polynomials. These polynomials are called the degenerate Apostol-Frobenius-type poly-Genocchi polynomials with parameters a and b. Several identities and formulas are derived including recurrence relations, explicit formulas and certain differential identity. Moreover, some relations are established connecting these polynomials to degenerate Stirling numbers of the first and second kind, higher order degenerate Bernoulli polynomials, and higher order degenerate Frobenius-Euler polynomials.