Communications of the
Korean Mathematical Society CKMS

In this article, a hybrid class of the $q$-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for $q$-Hermite based Apostol type Frobenius-Genocchi polynomials of order $\alpha$ associated with $q$-Apostol Bernoulli polynomials, $q$-Apostol Euler polynomials and $q$-Apostol Genocchi polynomials

Keywords: $q$-Hermite polynomials, Apostol type $q$-Frobenius Genocchi polynomials, $q$-Hermite based Apostol type Frobenius-Genocchi polynomials

MSC numbers: Primary 05A30, 11B68, 11B73, 11B83, 33C45

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning (No. 2017R1E1A1A03070483).