(untitled) (European Journal of Pure and Applied Mathematics, 2025)
This paper introduces a novel variation of poly-Genocchi polyno- mials by combining elements from the modified degenerate polyexpo- nential function, Hermite-Based Apostol-Genocchi polynomials, and Frobenius polynomials. These newly formulated polynomials, termed as the degenerate Hermite-Based Apostol-Frobenius-type poly-Genocchi polynomials with parameters a, b, and c, are explored to derive various identities and formulas. These include recurrence relations, explicit formulas, and specific differential identities. Furthermore, the pa- per establishes connections between these polynomials and degenerate Stirling numbers of the first and second kind, higher-order degenerate Bernoulli polynomials, and higher-order degenerate Frobenius-Euler polynomials.