Developing a Series Solution Method of q-Difference Equations

الملخص EN

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.