On Apostol-Type Multi Poly-Genocchi Polynomials with Parameters a,b, and c (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we investigate and analyze the Apostol numbers and polynomials, extending these properties by integrating them with the multi-polylogarithm function. Through this approach, we establish new properties and introduce a novel concept, which we refer to as the Apostol-type multi-poly Genocchi polynomials with parameters a, b, and c. Several properties of these polynomials are established including identities, the relation to Bernoulli polynomials, including some recurrence relations, addition and explicit formulas which are parallel on generalized poly-Genocchi polynomials.
Keywords: poly-Genocchi polynomials; multi-poly-Genocchi polynomials; Apostol type polynomials