# §4.47 Approximations

## §4.47(i) Chebyshev-Series Expansions

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

## §4.47(ii) Rational Functions

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

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