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

Mohd Abdur RASHID  Masao KODAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.9   pp.2303-2310
Publication Date: 2001/09/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
Keyword: 
cylindrical function,  asymptotic series,  numerical calculation,  transitional region,  

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Summary: 
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 Bmx) 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 Bmx) of arbitrary m. We developed a method of calculating Bmx) for arbitrary m, and then succeeded in calculating the cylindrical functions in the region νx with high precision.