# §11.15 Approximations

## §11.15(i) Expansions in Chebyshev Series

• Luke (1975, pp. 416–421) gives Chebyshev-series expansions for , , , and , , for ; , , , and , , ; the coefficients are to 20D.

• MacLeod (1993) gives Chebyshev-series expansions for , , , and , , ; the coefficients are to 20D.

## §11.15(ii) Rational and Polynomial Approximations

• Newman (1984) gives polynomial approximations for for , , and rational-fraction approximations for for , . The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.