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RSolve

FilledSmallSquare RSolve[eqn, a[n], n] solves a recurrence equation for a[n].

FilledSmallSquare RSolve[, , ... , [n], [n], ... , n] solves a system of recurrence equations.

FilledSmallSquare RSolve[eqn, a[, , ... ], , , ... ] solves a partial recurrence equation.

FilledSmallSquare RSolve[eqn, a, n] gives solutions for a as pure functions.

FilledSmallSquare 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].

FilledSmallSquare Equations such as a[0]==val can be given to specify end conditions.

FilledSmallSquare If not enough end conditions are specified, RSolve will give general solutions in which undetermined constants are introduced.

FilledSmallSquare 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], ... .

FilledSmallSquare GeneratedParameters->(Module[{C}, C]&) guarantees that the constants of integration are unique, even across different invocations of RSolve.

FilledSmallSquare For partial recurrence equations, RSolve generates arbitrary functions C[n][... ].

FilledSmallSquare 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.

FilledSmallSquare RSolve sometimes gives implicit solutions in terms of Solve.

FilledSmallSquare RSolve handles both ordinary difference equations and -difference equations.

FilledSmallSquare RSolve handles difference-algebraic equations as well as ordinary difference equations.

FilledSmallSquare 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.

FilledSmallSquare See Section 1.5.13 and Section 3.6.8.

FilledSmallSquare Implementation Notes: see Section A.9.5.

FilledSmallSquare See also: Sum, ZTransform, DSolve.

FilledSmallSquare New in Version 5.0.

Further Examples