# Discrete q-derivatives and symmetries of q-difference equations

@article{Levi2003DiscreteQA, title={Discrete q-derivatives and symmetries of q-difference equations}, author={Decio Levi and J. Negro and Mariano A. del Olmo}, journal={Journal of Physics A}, year={2003}, volume={37}, pages={3459-3473} }

In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many properties considered for shift invariant difference operators satisfying the umbral calculus can be implemented to the case of the q-difference operators. This q-umbral calculus can be used to provide solutions to linear q-difference equations and q-differential delay equations. To illustrate the method, we will apply the obtained results to… Expand

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