Chebyshev expansions for the Bessel function $J_{n}(z)$ in the complex plane
Authors:
J. P. Coleman and A. J. Monaghan
Journal:
Math. Comp. 40 (1983), 343366
MSC:
Primary 65A05; Secondary 30E10, 33A40, 65D20
DOI:
https://doi.org/10.1090/S00255718198306794514
MathSciNet review:
679451
Fulltext PDF Free Access
Abstract  References  Similar Articles  Additional Information
Abstract: Polynomialbased approximations for ${J_0}(z)$ and ${J_1}(z)$ are presented. The first quadrant of the complex plane is divided into six sectors, and separate approximations are given for $z \leqslant 8$ and for $z \geqslant 8$ on each sector. Each approximation is based on a Chebyshev expansion in which the argument of the Chebyshev polynomials is real on the central ray of the sector. The errors involved in extrapolation off the central ray are discussed. The approximation obtained for $z \geqslant 8$ can also be used to evaluate the Bessel functions ${Y_0}(z)$ and ${Y_1}(z)$ and the Hankel functions of the first and second kinds.

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Article copyright:
© Copyright 1983
American Mathematical Society