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

This paper intends to define degenerate q-Hermite polynomials, namely polynomials by means of generating function. Some significant properties such as recurrence relations, explicit identities and differential equations are established. Many mathematicians have been studying the arising from functions special numbers polynomials. Based on results so far, we find for We also provide some using coefficients this equation. Finally, use a computer view location zeros in equations. Numerical experiments confirmed that roots q-Hermit not symmetric with respect imaginary axis.