extend a series solution of a q-difference equation to higher degree
ExtendSeries(sol, data, deg, dataname)
formal series solution of the system that is the result of an invocation of SeriesSolution or ExtendSeries
special data needed to extend the series, returned by SeriesSolution or ExtendSeries
positive integer; formal degree of the initial terms to extend to
(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]
The ExtendSeries command returns the initial terms of the formal series solution sol extended to the specified formal degree deg.
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.
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.
The solution is a series expansion in x, corresponding to var. The order term (for example O⁡x6) is the last term in the series. For the system case the solution is a list of such series expansions.
eq ≔ y⁡q⁢x−1+x2⁢y⁡x
eq ≔ y⁡q⁢x−x2+1⁢y⁡x
var ≔ y⁡x
sol ≔ SeriesSolution⁡eq,var,,output=basis_C,'data'
sol ≔ _C1+O⁡x
sol ≔ ExtendSeries⁡sol,data,4,'data'
sol ≔ _C1+_C1⁢x2q2−1+_C1⁢x4q2−1⁢q4−1+O⁡x5
eq ≔ 1−q10−q−q10⁢x⁢y⁡q2⁢x−1−q20−q2−q20⁢x⁢y⁡q⁢x+q10⁢1−q10−q2−q11⁢x⁢y⁡x=q21−q20−q12+q10+q2−q⁢x+x20
eq ≔ 1−q10−−q10+q⁢x⁢y⁡q2⁢x−1−q20−−q20+q2⁢x⁢y⁡q⁢x+q10⁢1−q10−−q11+q2⁢x⁢y⁡x=q21−q20−q12+q10+q2−q⁢x+x20
sol ≔ SeriesSolution⁡eq,var,output=onesol,'data'
sol ≔ 1+x10+O⁡x11
sol ≔ ExtendSeries⁡sol,data,20
sol ≔ x10+1−x20q10⁢q40−2⁢q30+2⁢q10−1+O⁡x21
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