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QDifferenceEquations[ExtendSeries] - extend a series solution of a q-difference equation to higher degree
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Calling Sequence
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ExtendSeries(sol, data, deg, dataname)
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Parameters
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sol
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formal series solution of the system that is the result of an invocation of SeriesSolution or ExtendSeries
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data
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special data needed to extend the series, returned by SeriesSolution or ExtendSeries
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deg
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positive integer; formal degree of the initial terms to extend to
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dataname
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(optional) name; if given the name is set to special data needed to extend the series found to higher degree with further invocation of QDifferenceEquations[ExtendSeries]
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Description
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The ExtendSeries command returns the initial terms of the formal series solution sol extended to the specified formal degree deg.
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Additionally, if a name given in the dataname parameter, the command sets the name to special data needed to extend the series found to higher degree with further invocation of QDifferenceEquations[ExtendSeries] command.
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The ExtendSeries 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[ExtendSeries] in order to find solutions.
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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.
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Examples
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![sol := SeriesSolution(eq, var, {}, output = basis[_C], 'data')](/support/helpjp/helpview.aspx?si=8737/file02638/math132.png)
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![sol := _C[1]+O(x)](/support/helpjp/helpview.aspx?si=8737/file02638/math135.png)
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![sol := _C[1]+_C[1]*x^2/(-1+q^2)+_C[1]*x^4/((-1+q^2)*(-1+q^4))+O(x^5)](/support/helpjp/helpview.aspx?si=8737/file02638/math142.png)
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