Error Estimations of Cylindrical Functions Calculated with Hankel's Asymptotic Expansions

Masao KODAMA  Hideomi TAKAHASHI  Kengo TAIRA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.1   pp.238-241
Publication Date: 1997/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Numerical Analysis and Optimization
cylindrical function,  Hankel's asymptotic expansion,  numerical calculation,  error analysis,  

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Hankel's asymptotic expansions are frequently used for numerical calculation of cylindrical functions of complex order. We beforehand need to estimate the precisions of the cylindrical functions calculated with Hankel's asymptotic expansions in order to use these expansions. This letter presents comparatively simple expressions for rough estimations of the errors of the cylindrical functions calculated with the asymptotic expansions, and features of the errors are discussed.