Exact Remainders for Asymptotic Expansions of Fractional Integrals

This is a continuation of work begun in an earlier paper inwhich we used the theory of distributions to derive explicitexpressions for the remainder terms associated with the asymptoticexpansions of the Stieltjes transform. In this paper similarresults are obtained for the fractional integral of order definedby 1f(x)=1/f()^x_o(x-)^x-1 f(t)dt, >. Heref(t) is a locally integrable function on 0, ) and satisfies f(t) a_st-5–0(ó >0), s=0 as