Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Very high accuracy Chebyshev expansions for the basic trigonometric functions

Author: J. L. Schonfelder
Journal: Math. Comp. 34 (1980), 237-244
MSC: Primary 65D20
MathSciNet review: 551302
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Chebyshev expansion coefficients, accurate to forty decimal places, for the functions sine, cosine, and tangent, are tabulated. The methods used to generate the expansions are outlined and the ways in which accuracy of the tabulated coefficients were checked are noted.

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

  • [1] C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London, 1962. MR 0142793
  • [2] Y. L. LUKE, The Special Functions and Their Approximations, Vols. 1, 2, Academic Press, New York, 1969.
  • [3] J. L. SCHONFELDER, "The production of special function routines for a multi-machine library," Software-Practical and Experience, vol. 6, 1976, pp. 71-82; "The production and testing of special function software in the NAG library" (Goos and Hartmanis, Eds.), Portability of Numerical Software, Lecture Notes in Computer Science, Vol. 57, Springer-Verlag, Berlin and New York, 1976.
  • [4] J. L. SCHONFELDER & J. T. THOMASON, "Applications support by direct language extension" (Gelenbe and Portier, Eds.), International Computing Symposium 1975, North-Holland, Amsterdam, 1975; "Arbitrary precision arithmetic in Algol 68," in Software--Practice and Experience, Vol. 9, No. 3, 1979, pp. 173-182.
  • [5] J. L. Schonfelder, Chebyshev expansions for the error and related functions, Math. Comp. 32 (1978), no. 144, 1232–1240. MR 0494846,
  • [6] L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London-New York-Toronto, Ont., 1968. MR 0228149
  • [7] J. L. SCHONFELDER, "Generation of high precision Chebyshev expansions." (In preparation.)
  • [8] Yudell L. Luke, Algorithms for the computation of mathematical functions, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0494840

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65D20

Retrieve articles in all journals with MSC: 65D20

Additional Information

Keywords: Chebyshev expansions, trigonometric functions, approximation
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society