4 Elementary Functions Computation 4.46 Tables 4.48 Software

§4.47 Approximations

Keywords:: exponential function, hyperbolic functions, inverse hyperbolic functions, inverse trigonometric functions, logarithm function, trigonometric functions
Permalink:: http://dlmf.nist.gov/4.47

§4.47(i) Chebyshev-Series Expansions
§4.47(ii) Rational Functions
§4.47(iii) Padé Approximations
§4.47(iv) Additional References

§4.47(i) Chebyshev-Series Expansions

Keywords:: Chebyshev-series expansions, exponential function, inverse hyperbolic functions, inverse trigonometric functions, logarithm function, trigonometric functions
Permalink:: http://dlmf.nist.gov/4.47.i

Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for $\mathop{\ln\/}\nolimits$ , $\mathop{\exp\/}\nolimits$ , $\mathop{\sin\/}\nolimits$ , $\mathop{\cos\/}\nolimits$ , $\mathop{\tan\/}\nolimits$ , $\mathop{\cot\/}\nolimits$ , $\mathop{\mathrm{arcsin}\/}\nolimits$ , $\mathop{\mathrm{arctan}\/}\nolimits$ , $\mathop{\mathrm{arcsinh}\/}\nolimits$ . Schonfelder (1980) gives 40D coefficients for $\mathop{\sin\/}\nolimits$ , $\mathop{\cos\/}\nolimits$ , $\mathop{\tan\/}\nolimits$ .

§4.47(ii) Rational Functions

Permalink:: http://dlmf.nist.gov/4.47.ii

Hart et al. (1968) give $\mathop{\ln\/}\nolimits$ , $\mathop{\exp\/}\nolimits$ , $\mathop{\sin\/}\nolimits$ , $\mathop{\cos\/}\nolimits$ , $\mathop{\tan\/}\nolimits$ , $\mathop{\cot\/}\nolimits$ , $\mathop{\mathrm{arcsin}\/}\nolimits$ , $\mathop{\mathrm{arccos}\/}\nolimits$ , $\mathop{\mathrm{arctan}\/}\nolimits$ , $\mathop{\sinh\/}\nolimits$ , $\mathop{\cosh\/}\nolimits$ , $\mathop{\tanh\/}\nolimits$ , $\mathop{\mathrm{arcsinh}\/}\nolimits$ , $\mathop{\mathrm{arccosh}\/}\nolimits$ . Precision is variable.

§4.47(iii) Padé Approximations

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Luke (1975, Chapter 3) supplies real and complex approximations for $\mathop{\ln\/}\nolimits$ , $\mathop{\exp\/}\nolimits$ , $\mathop{\sin\/}\nolimits$ , $\mathop{\cos\/}\nolimits$ , $\mathop{\tan\/}\nolimits$ , $\mathop{\mathrm{arctan}\/}\nolimits$ , $\mathop{\mathrm{arcsinh}\/}\nolimits$ . Precision is variable.

§4.47(iv) Additional References

Permalink:: http://dlmf.nist.gov/4.47.iv

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

§4.47 Approximations

Contents

§4.47(i) Chebyshev-Series Expansions

§4.47(ii) Rational Functions

§4.47(iii) Padé Approximations

§4.47(iv) Additional References