Developing a Series Solution Method of q -Difference Equations

Abstract

The series solution is widely applied to differential equations on $ℝ$ but is not found in $q$-differential equations. Applying the Taylor and multiplication rule of two generalized polynomials, we develop a series solution of linear homogeneous $q$-difference equations. As an example, the series solution method is used to find a series solution of the second-order $q$-difference equation of Hermite’s type.