*Article* **Differential Equations Associated with Two Variable Degenerate Hermite Polynomials**

**Kyung-Won Hwang 1 and Cheon Seoung Ryoo 2,\***

1 Department of Mathematics, Dong-A University, Busan 604-714, Korea; khwang@dau.ac.kr

2 Department of Mathematics, Hannam University, Daejeon 34430, Korea

**\*** Correspondence: ryoocs@hnu.kr

Received: 14 January 2020; Accepted: 5 February 2020; Published: 10 February 2020

**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

**MSC:** 05A19; 11B83; 34A30; 65L99
