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

Abstract

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.

Keywords

• $ (q， h) $-derivative
• degenerate quantum genocchi (dqg) polynomials
• approximate root
• $ (q， h) $-difference equation