There are so many methods of calculating the cylindrical function Zν(x), but it seems that there is no method of calculating Zν(x) in the region of νx and |ν|»1 with high accuracy. The asymptotic series presented by Watson, et al. are frequently used for the numerical calculation of cylindrical function Zν(x) where νx and |ν|»1. However, the function Bm(εx) included in the m'th term of the asymptotic series is known only for m5. Hence, the asymptotic series can not give sufficiently accurate values of the cylindrical functions. The authors attempt to develop programs for the numerical calculation of the cylindrical functions using this asymptotic series. For this purpose, we must know the function Bm(εx) of arbitrary m. We developed a method of calculating Bm(εx) for arbitrary m, and then succeeded in calculating the cylindrical functions in the region νx with high precision.