Very high accuracy Chebyshev expansions for the basic trigonometric functions
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Chebyshev expansion coefficients, accurate to forty decimal places, for the functions sine, cosine, and tangent, are tabulated in this paper, and the methods used to generate the expansions are outlined and the ways in which accuracy of the tabulated coefficients were checked are noted.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.read more
Citations
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Journal ArticleDOI
The Special Functions and Their Approximations (Vols. I & II Yudell L. Luke)
Journal ArticleDOI
Chebyshev series expansion of inverse polynomials
TL;DR: The Chebyshev series expansion of the inverse of a polynomial is well defined in this paper, and it is shown that finding the bj in f(x)/Σ0k bj Tj(x) = 1 + Σk+1∞ an Tn(x); a Newton algorithm can produce these if the Chebyhev expansion of f (x) is known.
Journal ArticleDOI
Semantic extension possibilities in the proposed new fortran
TL;DR: The scope provided by the proposed new features for 'semantic extension' of the Fortran language is looked at, illustrated by way of example code which could provide an extended‐precision numeric facility if implemented.
Journal ArticleDOI
Ultra-high precision computations
H.G. Khajah,E.L. Ortiz +1 more
TL;DR: A recently devised technique for the sharp determination of upper and lower error bounds for Tau Method approximations enables us to find the degree n required to achieve a prescribed accuracy ϵ over a given interval.
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Variable precision arithmetic: a Fortran 95 module
TL;DR: The design and development of a software package supporting variable precision arithmetic as a semantic extension to the core FORTRAN language and the working precision of the arithmetic supported by this package can be dynamically and arbitrarily variable.
References
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Journal ArticleDOI
The special functions and their approximations
C. W. Clenshaw,Yudell L. Luke +1 more
Book
Algorithms for the Computation of Mathematical Functions
TL;DR: 43. Mathematical Functions and Their Approximations by Yudell L. Luke, 1976-06 44. Algorithms for the Computation of Mathematical functions by Yuda L Luke, 1977 45. Integrals of Bessel functions byYudellL Luke, 1962 46.