How to solve for the analytic solution of a recurrence relation in mathematica -
i have recurrence such following: rsolve[{f[m, n] == f[m, n - 1] + f[m - 1, n], f[0, n] == 1, f[m, 0] == 1}, f[m, n], {n}] i tried use rsolve, got error: rsolve::deqx: supplied equations not difference equations of given functions. appreciate help! the difference equation , initial conditions mathematica (7 , 8) not solving it... both , without initial conditions. rsolve expressions left unevaluated in[1]:= rsolve[{f[m,n]==f[m,n-1]+f[m-1,n],f[0,n]==f[m,0]==1},f[m,n],{m,n}] rsolve[{f[m,n]==f[m,n-1]+f[m-1,n]},f[m,n],{m,n}] out[1]= rsolve[{f[m,n]==f[-1+m,n]+f[m,-1+n],f[0,n]==f[m,0]==1},f[m,n],{m,n}] out[2]= rsolve[{f[m,n]==f[-1+m,n]+f[m,-1+n]},f[m,n],{m,n}] i know mathematica uses generating functional methods (probably among other things) solve such recurrences, don't know why fails in such simple case. so let's hand. let g(x,n) generating function f(m,n) now examine sum of f(m+1,n) x^m now solve simpl...