3
$\begingroup$

I'd like to employ another symbol (say alpha or k) instead of n in the following (type of) function:

DifferenceRoot[
  Function[{\[FormalY], \[FormalN]},
    {2 + 3 \[FormalN] - 2 \[FormalN]^2 - \[FormalN]^3 - (1 + \[FormalN]) (2 + \[FormalN])
     \[FormalY][\[FormalN]] + \[FormalN] (1 + \[FormalN]) (2 + \[FormalN])
     \[FormalY][1 + \[FormalN]] == 0, \[FormalY][1] == 0}
   ]
 ][n]
$\endgroup$
9
$\begingroup$

There is a hidden option to change the variables used by DifferenceRoot[]:

SetSystemOptions["HolonomicOptions" -> {"IteratorSymbol" -> k, "SequenceSymbol" -> ϕ}];

after which

DifferenceRootReduce[n!, n]
   (* DifferenceRoot[Function[{ϕ, k}, {(-1 - k) ϕ[k] + ϕ[1 + k] == 0, ϕ[0] == 1}]][n] *)

For the analogous case of DifferentialRoot[], the corresponding options are "VariableSymbol" and "FunctionSymbol".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.