# RSolveValue

RSolveValue[eqn,expr,n]

gives the value of expr determined by a symbolic solution to the ordinary difference equation eqn with independent variable n.

RSolveValue[{eqn1,eqn2,},expr,]

uses a symbolic solution for a list of difference equations.

RSolveValue[eqn,expr,{n1,n2,}]

uses a solution for the partial recurrence equation eqn.

# Details and Options

• RSolveValue[eqn,a,n] gives a solution for a as a pure function.
• The equations can involve objects of the form a[n+λ], where λ is a constant, or in general, objects of the form a[ψ[n]], a[ψ[ψ[n]], a[ψ[[ψ[n]]]], where ψ can have forms such as:
•  n+λ arithmetic difference equation μ n geometric or -difference equation μ n+λ arithmetic-geometric functional difference equation μ nα geometric-power functional difference equation linear fractional functional difference equation
• Equations such as a[0]==val can be given to specify end conditions.
• If not enough end conditions are specified, RSolveValue will use general solutions in which undetermined constants are introduced.
• The constants introduced by RSolveValue are indexed by successive integers. The option GeneratedParameters specifies the function to apply to each index. The default is , which yields constants C[1], C[2], .
• GeneratedParameters->(Module[{C},C]&) guarantees that the constants of integration are unique, even across different invocations of RSolveValue.
• For partial recurrence equations, RSolveValue generates arbitrary functions C[n][].
• Solutions given by RSolveValue sometimes include sums that cannot be carried out explicitly by Sum. Dummy variables with local names are used in such sums.
• RSolveValue handles both ordinary difference equations and difference equations.
• RSolveValue handles differencealgebraic equations, as well as ordinary difference equations.
• RSolveValue can solve linear recurrence equations of any order with constant coefficients. It can also solve many linear equations up to second order with nonconstant coefficients, as well as many nonlinear equations.

# Examples

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## Basic Examples(4)

Solve a difference equation:

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Include a boundary condition:

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Get a "pure function" solution for a:

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Plot the solution:

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Solve a functional equation:

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Obtain the value of the solution at a point:

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List of values:

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# Tutorials

Introduced in 2014
(10.0)