Developing a series solution method of \(q\)-difference equations. (English) Zbl 1266.39008

Summary: The series solution is widely applied to differential equations on \(\mathbb R\) 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.


39A13 Difference equations, scaling (\(q\)-differences)
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