I guess a recurrence relation is a special case of a functional equation. I didn't consider that a functional equation might be transformable to a recurrence relation via a change of variable.
I'm not sure how well your way works. If you take the classical functional equation f(a + b) = f(a)*f(b), we let k*(x + 1) = a, k*x = b, and we get f(k*(2*x + 1) = f(k*x) + f(k*(x + 1)). SymPy's rsolve cannot solve this (even if you set k = 1). Maybe it is solvable though. Aaron Meurer On Tue, May 28, 2013 at 12:16 PM, F. B. <franz.bona...@gmail.com> wrote: > If the functional equation contains f(a) and f(b), it can be reduced to a > recurrence formula by > > k (x + 1) = a > k x = b > > which is > > k = a - b > x = b / (a - b) > > now the new function g(x) = f(k*x) displays the same equation as a > recurrence equation [ g(x) = f(b), g(x+1) = f(a) ]. > > That was just an attempt, but I think there must be a reason why Wolfram > makes RSolve solve both recurrence and functional equations. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at http://groups.google.com/group/sympy?hl=en-US. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
