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LREtools

  

constcoeffsol

  

find all solutions of linear recurrence equations with constant coefficients

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

constcoeffsol(problem)

Parameters

problem

-

problem statement or RESol for a single equation in a single recurrence variable

Description

• 

Finds all solutions of the linear recurrence equation with constant coefficients.

• 

Optionally, one can specify output=basis  or output=gensol, which specifies respectively that one wants a basis of the solutions or a generic solution.  The initial conditions that may be associated to the problem are only used in the generic solution case.  Arbitrary constants for the basis case are represented as _C[1], _C[2], ..., _C[n], where the _C is an escaped local variable.

• 

See the help page for LREtools[REcreate] for the definition of the format of a problem.

Examples

withLREtools:

recan9an+1+26an+234an+3+21an+45an+5=0:

constcoeffsolrec,an,

3125a42563125a0256+3125a1649375a2128+3125a36415n5+5a44+a042a1+9a224a3n+1n+2n+3685a416+21a01641a14+175a2873a34n+1n+22+565a464+181a064341a116+1343a232517a316n+11845a4256821a0256+1461a1645023a2128+1781a364

(1)

recan+4=an+3+3an+2+5an+1+2an:

constcoeffsolrec,an,

13a3274a29+14a19+68a027−1n+a33+a1+2a03−1nn+1n+22+7a39+a238a1320a09−1nn+12a354a218a118a0542n

(2)

recan+22an+1an=0:

constcoeffsolrec,an,

_α=RootOf_Z2+2_Z13a0+a1_α+a0a1_αn_α4

(3)

See Also

LREtools

LREtools[REcreate]

RESol

rsolve