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QDifferenceEquations

  

ExtendSeries

  

extend a series solution of a q-difference equation to higher degree

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ExtendSeries(sol, data, deg, dataname)

Parameters

sol

-

formal series solution of the system that is the result of an invocation of SeriesSolution or ExtendSeries

data

-

special data needed to extend the series, returned by SeriesSolution or ExtendSeries

deg

-

positive integer; formal degree of the initial terms to extend to

dataname

-

(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]

Description

• 

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 Ox6) is the last term in the series. For the system case the solution is a list of such series expansions.

Examples

withQDifferenceEquations:

eqyqx1+x2yx

eq:=yqxx2+1yx

(1)

varyx

var:=yx

(2)

solSeriesSolutioneq,var,,output=basis_C,'data'

sol:=_C1+Ox

(3)

solExtendSeriessol,data,4,'data'

sol:=_C1+_C1x2q21+_C1x4q21q41+Ox5

(4)

eq1q10qq10xyq2x1q20q2q20xyqx+q101q10q2q11xyx=q21q20q12+q10+q2qx+x20

eq:=1q10q10+qxyq2x1q20q20+q2xyqx+q101q10q11+q2xyx=q21q20q12+q10+q2qx+x20

(5)

varyx

var:=yx

(6)

solSeriesSolutioneq,var,output=onesol,'data'

sol:=1+x10+Ox11

(7)

solExtendSeriessol,data,20

sol:=x10+1x20q10q402q30+2q101+Ox21

(8)

See Also

LinearFunctionalSystems[ExtendSeries]

LinearFunctionalSystems[SeriesSolution]

QDifferenceEquations

QDifferenceEquations[SeriesSolution]

 


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