... I. Gy¨ori, and G. Ladas, Eds., pp. 567–577, Gordon and Breach, Amsterdam, The Netherlands,1997.10 C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers,International ... k>0, and in the second case as k<0 where k 2p − q. The whole proof of the result is too long tounderstand, so we divide the estimations into two parts, part I this paper and part II the next ... α2−Nk1.4.24Now we completed the estimate of the error bounds for asymptotic solutions to secondorder linear difference equations in the first case. For the second case, we leave it to the secondpart of...