A New Class of Hermite-Apostol Type Frobenius-Euler Polynomials and Its Applications

Abstract

The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite⁻Apostol-type Frobenius⁻Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz⁻Lerch Zeta functions and some summation formulae related to these polynomials are derived. Further, we establish certain symmetry identities involving generalized power sums and Hurwitz⁻Lerch Zeta functions. An operational view for these polynomials is presented, and corresponding applications are given. The illustrative special cases are also mentioned along with their generating equations.

Keywords

• Apostol-type Frobenius–Euler polynomials
• three-variable Hermite polynomials
• symmetric identities
• explicit relations
• operational connection