How do I solve a linear multivariable recurrence relation like the following: $$ f(x, y) = a f(x - 1, y) + b f(y - 1, x) + c $$ subject to the boundary conditions: $$ f(x, 0) = 0, f(0, y) = 1 $$ Assuming $a, b, c$ are all real (possible negative).
I'm not even sure it's possible to do, so if that's true I'd like to know that as well.