Miniaturized Tables of Bessel Functions

In this report, we discuss the representation of bivariate functions in double series of Chebyshev polynomials. For an application, we tabulate coefficients which are accurate to 20 decimals for the evaluation of (2z/π)1/2 ez Kν(z) for all z ≥ 5 and all ν, 0 ≤ ν ≤ 1. Since Kν(z) is an even function...

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Bibliographic Details
Published in:Mathematics of computation 1971, Vol.25 (114), p.323-330
Main Author: Luke, Yudell L.
Format: Article
Language:English
Subjects:
Approximation
Bessel functions
Coefficients
Mathematical functions
Mathematical independent variables
Mathematical tables
Miniaturization
Polynomials
Series convergence
Series expansion
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Summary:In this report, we discuss the representation of bivariate functions in double series of Chebyshev polynomials. For an application, we tabulate coefficients which are accurate to 20 decimals for the evaluation of (2z/π)1/2 ez Kν(z) for all z ≥ 5 and all ν, 0 ≤ ν ≤ 1. Since Kν(z) is an even function in ν and satisfies a three-term recurrence formula in ν which is stable when used in the forward direction, we can readily evaluate Kν(z) for all z ≥ 5 and all ν ≥ 0. Only 205 coefficients are required to achieve an accuracy of about 20 decimals for the z and ν ranges described. Extension of these ideas for the evaluation of all Bessel functions and other important bivariate functions is under way.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1971-0295508-6