Some properties for 2-variable modified partially degenerate Hermite (MPDH) polynomials derived from differential equations and their zeros distributions

Abstract

The 2-variable modified partially degenerate Hermite (MPDH) polynomials are the subject of our study in this paper. We found basic properties of these polynomials and obtained several types of differential equations related to MPDH polynomials. Based on the MPDH polynomials, we looked at the structures of the approximation roots for a particular polynomial and checked the values of the approximate roots. Further, we presented some conjectures for MPDH polynomials.

Keywords

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