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 A new class of $q$-Hermite-based Apostol type Frobenius Genocchi polynomials Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 759-771 https://doi.org/10.4134/CKMS.c190436Published online July 2, 2020Printed July 31, 2020 Jung Yoog Kang, Waseem A. Khan Silla University; Prince Mohammad Bin Fahd University Abstract : 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). Downloads: Full-text PDF   Full-text HTML