The law of the iterated logarithm for certain power series and generalized Norlund methods

Let (p(n)) be a sequence of real numbers with p(n) similar to R(n), R(.) a regulary varying function with index greater than -1/2. We prove the Hartman-Wintner law of the iterated logarithm fur the corresponding (J(p)) power series transform and generalized Norlund transforms (N-beta p) of sequences (X(n)) of i.i.d. random variables with mean-zero and variance 1. We also identify the cluster sets.