New Algorithm on the Recurrence Method for Numerial Calculation of Bessel Function of Complex Order

Masao KODAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.4   pp.621-623
Publication Date: 1996/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Numerical Analysis and Optimization
Bessel function,  recurrence method,  numerical calculation,  

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The recurrence method is useful for numerical calculation of the Bassel function Jv(x) of complex order v. The necessary total number of the recurrences in this method has been examined for the real order v, but it is known only for limited ranges of the real order v and the variable x, and it is not known for the complex order v. This letter proposes a new algorithm which increases the total number of the recurrences gradually, and which stops the calculation automatically when the approximate Bessel function with a necessary precision is obtained.