The SeriesSolution command returns the series solution of the given linear q-difference equation with polynomial coefficients. If such a solution does not exist, then NULL is returned.

Additionally, if a name given in the dataname parameter, then the command sets the name to special data needed to extend the series found to higher degree with QDifferenceEquations[ExtendSeries] command.

The SeriesSolution command solves the problem with a single q-difference equation and also with a system of such equations. In the latter case the command invokes LinearFunctionalSystems[SeriesSolution] in order to find solutions.

The solution is a series expansions in x, corresponding to var. The order term (for example ) is the last term in the series. For the system case the solution is a list of such series expansions.

For a single q-difference equation the function computes some initial terms of the series. The number of the terms is determined in such a way that the process of computing the successive terms does not lead to new arbitrary constants. The successive terms can be computed with the QDifferenceEquations[ExtendSeries].

The parameter q in a scalar q-difference equation can be either a name or a rational number.

Optionally, you can specify output=basis, output=basis[var], output=onesol, output=gensol, or output=anysol.

output=basis[C]

The output is provided as a single algebraic expression that is a -linear combination of the independent solutions plus any particular solution for the inhomogeneous case. The independent solutions will have indexed coefficients of the form , where var is as provided in the output=basis[C] option.

output=onesol

This specifies that only a single solution be provided as output.

The inits argument is in fact ignored and allowed in the calling sequence for compatibility with the other solvers in the package.