Chebyshev%20polynomials
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1: 18.5 Explicit Representations
2: 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.
3: 7.24 Approximations
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
… ►Bulirsch (1967) provides Chebyshev coefficients for the auxiliary functions and for (15D).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
4: 6.20 Approximations
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.
§6.20(ii) Expansions in Chebyshev Series
… ►Luke and Wimp (1963) covers for (20D), and and for (20D).