convert a recurrence into a differential equation
REtoDE(problem, f(z), output=val)
either a RESol recurrence structure, or a recurrence definition
name and variable of the function
form of the output, where output=DESol or output=diff
This routine returns the differential operator or differential equation satisfied by the generating function associated to the recurrence. This operator is returned as either a DESol operator or a differential equation (both possibly with initial conditions). No attempt is made to explicitly solve the result.
For the definition of the format of a problem, see the help page for LREtools[REcreate]. The problem can be an RESol structure resulting from a call to LREtools[REcreate].
The output option val can be either DESol which requests operator output (the default) or diff which requests the output in terms of a differential system.
Note: In some cases initial conditions are also needed, so the output=diff result is returned as a set. If no initial conditions are needed, the output is a single ODE.
Note: This command performs the same operation as gfun[rectodiffeq] and the inverse operation is provided by gfun[diffeqtorec].
rec ≔ REcreate⁡a⁡n+2−2⁢a⁡n+1+a⁡n=0,a⁡n,
An example with conditions:
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