Numerical Calculation of the Bessel Function of Complex Order Using the Recurrence Method

Masao KODAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A   No.4   pp.506-516
Publication Date: 1995/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
Bessel function,  recurrence method,  numerical calculation,  error analysis,  

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First, the necessity of examining the numerical calculation of the Bessel function Jν(x) of complex order ν is explained. Second, the possibility of the numerical calculation of Jν(x) of arbitrary complex order ν by the use of the recurrence formula is ascertained. The rounding error of Jν(x) calculated by this method is investigated next by means of theory and numerical experiments when the upper limit of recurrence is sufficiently large. As a result, it was known that there is the possibility that the rounding error grows considerably when ν is complex. Counterplans against the growth of the rounding error will be described.