6

RSolveis the function you're looking for. The second example evaluates to Z = RSolveValue[{z[i + 1] == b z[i] + (1 - b) y[i], z[1] == 0}, z , i] (*Function[{i}, b^(-1 + i) (\!\(\*UnderoverscriptBox[\(\[Sum]\), \(K[1] = 0\), \(\(-1\) +i\)]\(-\((\((\(-1\) + b)\)\ \*SuperscriptBox[\(b\), \(-K[1]\)]\ y[K[1]])\)\)\) -y[0] + b y[0])]*) Z[1]//Simplify (*0*) ...


Only top voted, non community-wiki answers of a minimum length are eligible