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1: 25.5 Integral Representations
§25.5 Integral Representations
►§25.5(i) In Terms of Elementary Functions
… ►§25.5(ii) In Terms of Other Functions
… ►For similar representations involving other theta functions see Erdélyi et al. (1954a, p. 339). ►In (25.5.15)–(25.5.19), , is the digamma function, and is Euler’s constant (§5.2). …2: 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 et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
§7.24(ii) Expansions in Chebyshev Series
…3: 6.20 Approximations
§6.20(i) Approximations in Terms of Elementary Functions
… ►Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
Luke (1969b, pp. 41–42) gives Chebyshev expansions of , , and for , . The coefficients are given in terms of series of Bessel functions.