The forms of $(q,h)$-difference equation and the roots structure of their solutions with degenerate quantum Genocchi polynomials

We construct a new type of Genocchi polynomials using degenerate quantum exponential functions and find various forms of $(q,h)$-difference equations with these polynomials as solutions. This paper includes properties of the symmetric structures of $(q,h)$-difference equations and also presents $(q,h)$-difference equations with other polynomials as coefficients. By understanding the approximate roots structure of degenerate quantum Genocchi polynomials (DQG), which are common solutions to various forms of $(q,h)$-difference equations, we identify the properties of the solutions.