# §4.47 Approximations

## §4.47(i) Chebyshev-Series Expansions

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

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.

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.