On Asymptotic Behavior of Regularly Varying Moments for Discrete Laws

For a discrete law F and large n, we investigate the asymptotic relation EX(n)(u)l(X-n) similar to C-mu(EXn)(mu)l(EXn), mu epsilon (a, b), C-mu > 0 (EXn -> infinity), where l(.) is an arbitrary slowly varying function. Then we prove that regularly varying moments for Power Series Distributions, generated by an entire function of finite order, satisfy the above relation with C-mu = 1 for each mu epsilon (0, infinity).