Digital Library of Mathematical Functions
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4 Elementary FunctionsComputation

§4.47 Approximations

Contents

§4.47(i) Chebyshev-Series Expansions

Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for ln, exp, sin, cos, tan, cot, arcsin, arctan, arcsinh. Schonfelder (1980) gives 40D coefficients for sin, cos, tan.

§4.47(ii) Rational Functions

Hart et al. (1968) give ln, exp, sin, cos, tan, cot, arcsin, arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh. Precision is variable.

§4.47(iii) Padé Approximations

Luke (1975, Chapter 3) supplies real and complex approximations for ln, exp, sin, cos, tan, arctan, arcsinh. Precision is variable.

§4.47(iv) Additional References

See Luke (1975, pp. 288–289) and Luke (1969b, pp.74–76).