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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.E84A
No.9
pp.23032310 Publication Date: 2001/09/01
Online ISSN:
DOI:
Print ISSN: 09168508 Type of Manuscript: PAPER Category: Numerical Analysis and Optimization Keyword: cylindrical function, asymptotic series, numerical calculation, transitional region,
Full Text: PDF(644.5KB)>>
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.

