Chebyshev expansions for the Bessel function $J_{n}(z)$ in the complex plane
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 by J. P. Coleman and A. J. Monaghan PDF
 Math. Comp. 40 (1983), 343366 Request permission
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.References

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Additional Information
 © Copyright 1983 American Mathematical Society
 Journal: Math. Comp. 40 (1983), 343366
 MSC: Primary 65A05; Secondary 30E10, 33A40, 65D20
 DOI: https://doi.org/10.1090/S00255718198306794514
 MathSciNet review: 679451