Developing a series solution method of q -difference equations

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. © 2013 hsuan-ku liu.