Note on the binomial partial difference equation.

Some formulas for the "general solution" to the binomial partial difference equation cm,n = cm-1,n + cm-1,n-1, are known in the literature. However, it seems that there is no such a formula on the most natural domain connected to the equation, that is, on the set D = {(m, n) ∈ N²0: 0 ≤ n ≤ m. By using a connection with the scalar linear first order difference equation we show that the equation on the domain D n f(0, 0)g, can be solved in closed form by presenting a formula for the solution in terms of the "side" values ck,0, ck,k, k∈ℕ. [ABSTRACT FROM AUTHOR]