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5.14.3  Values of a recurrence relation or a system: rsolve

See also section 5.14.2

The rsolve command takes three arguments; an equation or list of equations that define a recurrence relation, the functions (with their variables) used, and equations for the starting values. For example, if a recurrence relation is defined by un+1 = f(un,n) with u0 = a, the arguments to rsolve will be u(n+1) = f(u(n),n), u(n) and u(0)=a. The recurrence relation must either be a homogeneous linear part with a nonhomogeneous part being a linear combination of polynomials in n times geometric terms in n (such as un+1 = 2 un + n 3n), or a linear fractional transformation (such as un+1 = (un−1)/(un−2)).
rsolve returns a matrix whose rows are the values of the sequence as functions of n.

Note that rsolve is more flexible than seqsolve since:

Examples:


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