Cheon Seoung Ryoo, R.P. Agarwal, and Jung Yoog Kang. Some Properties Involving 2-Variable Modified Partially Degenerate Hermite Polynomials Derived from Differential Equations and Distribution of Their Zeros. Dynamic Systems and Applications 29 (2020), No. 2, 248-269

https://doi.org/10.46719/dsa20202924

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

AMS (MOS) Subject Classification. 05A19, 11B83, 34A30, 65L99.