In a recent paper the author [1] extended an early result of Stieltjes, as an aid in the calculation of Bessel functions of orders 0 and 1 from their truncated asymptotic expansions. It is the purpose of this short note to extend these results to include modified Bessel functions. Inasmuch as the derivation of these results is essentially the same as that in the paper by Stieltjes [2], we shall merely outline the final results in the usual notation.