This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

RSolve

 RSolve[eqn, a[n], n]solves a recurrence equation for a[n]. RSolve[{eqn1, eqn2, ...}, {a1[n], a2[n], ...}, n]solves a system of recurrence equations. RSolve[eqn, a[n1, n2, ...], {n1, n2, ...}]solves a partial recurrence equation.
• RSolve[eqn, a, n] gives solutions for a as pure functions.
• The equations can involve objects of the form a[n+i] where i is any fixed integer, or objects of the form a[q^in].
• Equations such as a[0]val can be given to specify end conditions.
• If not enough end conditions are specified, RSolve will give general solutions in which undetermined constants are introduced.
• The constants introduced by RSolve 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], ... .
• For partial recurrence equations, RSolve generates arbitrary functions C[n][...].
• Solutions given by RSolve sometimes include sums that cannot be carried out explicitly by Sum. Dummy variables with local names are used in such sums.
• RSolve sometimes gives implicit solutions in terms of Solve.
• RSolve handles both ordinary difference equations and q-difference equations.
• RSolve handles difference-algebraic equations as well as ordinary difference equations.
• RSolve can solve linear recurrence equations of any order with constant coefficients. It can also solve many linear equations up to second order with non-constant coefficients, as well as many nonlinear equations.
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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Substitute the solution into an expression:
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 Scope   (25)
 Options   (1)
 Applications   (10)
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