Chebyshev expansions for the Bessel function in the complex plane

Authors:
J. P. Coleman and A. J. Monaghan

Journal:
Math. Comp. **40** (1983), 343-366

MSC:
Primary 65A05; Secondary 30E10, 33A40, 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1983-0679451-4

MathSciNet review:
679451

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Abstract: Polynomial-based approximations for and are presented. The first quadrant of the complex plane is divided into six sectors, and separate approximations are given for and for 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 can also be used to evaluate the Bessel functions and and the Hankel functions of the first and second kinds.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0679451-4

Article copyright:
© Copyright 1983
American Mathematical Society