Numerical Calculation of Cylindrical Functions in the Transitional Regions Using Asymptotic Series

Mohd Abdur RASHID, Masao KODAMA

Summary :

There are so many methods of calculating the cylindrical function Z_ν(x), but it seems that there is no method of calculating Z_ν(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 Z_ν(x) where νx and |ν|»1. However, the function B_m(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 B_m(εx) of arbitrary m. We developed a method of calculating B_m(εx) for arbitrary m, and then succeeded in calculating the cylindrical functions in the region νx with high precision.

• Publication: IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.9 pp.2303-2310
• Publication Date: 2001/09/01
• Type of Manuscript: PAPER
• Category: Numerical Analysis and Optimization

Authors

Mohd Abdur RASHID
Masao KODAMA

Keyword

cylindrical function,  asymptotic series,  numerical calculation,  transitional region