Asymptotic Expansions of Central Binomial Coefficents and Catalan Numbers

We give systematic view of the asymptotic expension of two well-known sequences,the central binomial coefficients and the Catalan numbers. The main Point is Explanation of the nature of the best shift in variable n,in order to obtain "nice" asymptotic expansions.we also give a complete asymptotic expansion of partial sums of these sequences.