Let a, b be two different complex numbers and (ck) be a sequence of complex numbers. We search for functions f(z) of exponential type satisfying In the case 3' = 1 there is a further solution )Co of a minimal type of order 1 or less than 1. All these functions are independent of each other. A solution of (1) which is independent of these functions can only be a polynomial of degree not greater than n. If 3' = 0 or 3' = oo a solution of (1) can only be a polynomial of degree not greater than n.Further we prove that there are solutions of exponential type if we have limk_.~o Ick -3'1 < P (P suitable).
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