Hermite-based hybrid polynomials and some related properties

In this paper, the two-variable one-parameter generalized Hermite-based hybrid polynomials are introduced by means of generating function, series definition and determinant definition. The recurrence relations, shift operators, differential, integro-differential and partial differential equations for these polynomials are established via factorization method. The two-variable one-parameter generalized Hermite-based Bernoulli, Euler and Genocchi polynomials are studied as the particular members and some examples are considered in terms of these polynomials to give the applications of main results. The graphical representation and interpretation is also shown for these polynomials.