Some Identities Involving 2-Variable Modified Degenerate Hermite Polynomials Arising from Differential Equations and Distribution of Their Zeros

In this chapter, we introduce the 2-variable modified degenerate Hermite polynomials and obtain some new symmetric identities for 2-variable modified degenerate Hermite polynomials. In order to give explicit identities for 2-variable modified degenerate Hermite polynomials, differential equations arising from the generating functions of 2-variable modified degenerate Hermite polynomials are studied. Finally, we investigate the structure and symmetry of the zeros of the 2-variable modified degenerate Hermite equations.