Differential Equations Associated with Two Variable Degenerate Hermite Polynomials

Abstract

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

Keywords

• differential equations
• symmetric identities
• degenerate hermite polynomials
• complex zeros