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Chebyshev approximations for the Riemann zeta function

Authors: W. J. Cody, K. E. Hillstrom and Henry C. Thacher
Journal: Math. Comp. 25 (1971), 537-547
MSC: Primary 65D20
MathSciNet review: 0295535
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Abstract: This paper presents well-conditioned rational Chebyshev approximations, involving at most one exponentiation, for computation of either $ \zeta (s) $ or $ \zeta (s) - 1,.5 \leqq s \leqq 55$, for up to 20 significant figures. The logarithmic error is required in one case. An algorithm for the Hurwitz zeta function, and an example of nearly double degeneracy are also given.

References [Enhancements On Off] (What's this?)

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  • [3] R. F. King & D. L. Phillips, ``The logarithmic error and Newton's method for the square root,'' Comm. ACM, v. 12, 1969, pp. 87-88. MR 0285109 (44:2333)
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Keywords: Rational Chebyshev approximations, Riemann zeta function, Hurwitz zeta function, logarithmic error, near degeneracy
Article copyright: © Copyright 1971 American Mathematical Society

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