# Generating Functions with multiple arguments

I want to solve the recurrence of Ackermann function using Generating Function in Mathematica.

GeneratingFunction[RSolve[{f[x, y] == f[x - 1, f[x, y - 1]],
f[0, y] == y + 1,f[x, 0] == f[x - 1, 1]},
f[x, y], x, y], x, y, n]


But I am not getting the result. As far as I know we can only pass 3 arguments to Generating Function but I am sending 4. Please let me know how to solve it.

P.S. I just started using Mathematica. So please suggest the solution though it is trivial.

• What is the definition for Rsolve? – Edmund Mar 5 '16 at 18:45
• I checked this question and thought I need to use Rsolve: stackoverflow.com/questions/4911900/… – siraj Mar 5 '16 at 18:51
• SiMemon, notice that the built-in Mathematica function is RSolve, notice the uppercase S. – MarcoB Mar 5 '16 at 18:57
• I changed it. But still I am getting error as "RSolve::nestdv: "The expression f[x,-1+y] has nested dependent variables. " – siraj Mar 5 '16 at 19:03
• RSolve cannot handle nested expressions, like f[x - 1, f[x, y - 1]]. Can you write your formula in another way? – bbgodfrey Mar 5 '16 at 19:15