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Convergence problems in the asymptotic expansions for the Bessel functions of complex argument
Author(s) -
Kausel Eduardo
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100619
Subject(s) - bessel function , convergence (economics) , argument (complex analysis) , mathematics , mathematical optimization , mathematical analysis , biochemistry , chemistry , economics , economic growth
The convergence of Hankel's asymptotic expansions for the Bessel functions of large complex argument are discussed, and a method is proposed to avoid numerical problems derived from their implementation in computer programs. Whiel the error tolerance cannot in all cases be controlled by the user, excellent results can indeed be obtained with application of the proposed method.