# §25.20 Approximations

• Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.

• Piessens and Branders (1972) gives the coefficients of the Chebyshev-series expansions of and , , for (23D).

• Luke (1969b, p. 306) gives coefficients in Chebyshev-series expansions that cover for (15D), for (20D), and 25.4) for (20D). For errata see Piessens and Branders (1972).

• Morris (1979) gives rational approximations for 25.12(i)) for . Precision is varied with a maximum of 24S.

• Antia (1993) gives minimax rational approximations for , where is the Fermi–Dirac integral (25.12.14), for the intervals and , with . For each there are three sets of approximations, with relative maximum errors .