# §7.24 Approximations

## §7.24(i) Approximations in Terms of Elementary Functions

• Hastings (1955) gives several minimax polynomial and rational approximations for , and the auxiliary functions and .

• Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.

• Cody (1968) gives minimax rational approximations for the Fresnel integrals (maximum relative precision 19S); for a Fortran algorithm and comments see Snyder (1993).

• Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).

## §7.24(ii) Expansions in Chebyshev Series

• Luke (1969b, pp. 323–324) covers and for (the Chebyshev coefficients are given to 20D); and for (the Chebyshev coefficients are given to 20D and 15D, respectively). Coefficients for the Fresnel integrals are given on pp. 328–330 (20D).

• Bulirsch (1967) provides Chebyshev coefficients for the auxiliary functions and for (15D).

• Schonfelder (1978) gives coefficients of Chebyshev expansions for on , for on , and for on (30D).

• Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).