RSolve
 Usage
• RSolve[eqn, a[n], n] solves a recurrence equation for a[n].
• RSolve[{ ,  , ... }, { [n],  [n], ... }, n] solves a system of recurrence equations.
• RSolve[eqn, a[ ,  , ... ], { ,  , ... }] solves a partial recurrence equation.
Notes
• 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^i n]. • 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 GeneratedParameters->C, which yields constants C[1], C[2], ... . • GeneratedParameters->(Module[{C}, C]&) guarantees that the constants of integration are unique, even across different invocations of RSolve. • 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  -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. • New in Version 5.
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