A new family of Apostol–Genocchi polynomials associated with their certain identities

Abstract

In this paper, we provide a generating function for mix type Apostol–Genocchi polynomials of order η associated with Bell polynomials. We also derive certain important identities of Apostol Genocchi polynomials of order η based on Bell polynomials, such as the correlation formula, the implicit summation formula, the derivative formula, some correlation with Stirling numbers and their special instances. Moreover, we discover some symmetric identities and their related known results.

Keywords

• generating function
• apostol–genocchi polynomials
• identities
• bell polynomials
• stirling numbers