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RESol - data structure to represent the solution of a recurrence equation
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Calling Sequence
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RESol(eqns, fcns, inits)
LREtools[REcreate](eqns, fcns, inits)
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Parameters
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eqns
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single equation or a set of equations
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fcns
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function name or set of function names
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inits
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set of initial conditions
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Description
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This data structure represents the solution of a recurrence equation. It is to rsolve and LREtools as DESol is to dsolve and DEtools.
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The parameters of an RESol are a set of normalized equations, a set of function names and a set of initial conditions.
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On output, an information table, INFO is added. The entries in this table are:
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type
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the strings 'linear' or 'nonlinear'
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functions
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a name or set of names of the recurrence function(s)
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vars
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a name or set of names of the recurrence variable(s)
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order
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the order of the equation
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shifteqn
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an equation in &Shift[vars](functions) which represents the shift operator associated to the linear recurrence equation
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coeffs
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a list of the rhs of the equation and the coefficients of the shifteqn
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Note that the first three items are always present, and the next three are there only if the recurrence is linear.
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Examples
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>
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| (1) |
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-n^2*a(n+1)+(n-17)*a(n) = sin(n), a(n), {a(0) = 0})](/support/helpjp/helpview.aspx?si=4752/file00126/math171.png)
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| (2) |
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![TABLE([vars = n, min_shift = 0, polycoeffs = false, nonvars = (), rhs = sin(n), max_shift = 2, order = 2, type = constcoeffs, coeffs = [-sin(n), n-17, -n^2, 1], functions = a, linear = true, shifteqn = `&Shift`[n](a)^2-n^2*`&Shift`[n](a)+n-17])](/support/helpjp/helpview.aspx?si=4752/file00126/math181.png)
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^2-a(n) = 0, a(n), {})](/support/helpjp/helpview.aspx?si=4752/file00126/math185.png)
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| (4) |
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![TABLE([vars = n, min_shift = 0, nonvars = (), max_shift = 2, order = 2, functions = a, linear = false])](/support/helpjp/helpview.aspx?si=4752/file00126/math195.png)
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