If t is restricted to the integers, the method is a special case of the Sonnenschein methods (Zeller and Beekman [-16], p. 185) and as such admits a probabilistic interpretation. As general references to probability theory we mention Chung [-2], Parzen [-11], Feller [-5], Breiman [,1]. Let X 1, X 2 . . . . be independent nonnegative integer valued random variables with common probability distribution given by P {X k =j} = pj. Let S, = X 1 +.. + X,, so that P {S, = h} = p~*, where the sequence {p~*, h > 0} is the n-fold convolution of the sequence {p j, j > 0}. The Sonnenschein method, associated with {p j}, is applied.to one-sided sequences by