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1: Bibliography Q
2: 20 Theta Functions
Chapter 20 Theta Functions
…3: Browsers
4: 3.11 Approximation Techniques
§3.11(i) Minimax Polynomial Approximations
… ►Then there exists a unique th degree polynomial , called the minimax (or best uniform) polynomial approximation to on , that minimizes , where . … ►§3.11(iii) Minimax Rational Approximations
… ►Then the minimax (or best uniform) rational approximation … ►Example
…5: 7.24 Approximations
§7.24 Approximations
… ►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).
6: 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(iii) Padé-Type and Rational Expansions
… ►Luke (1969b, pp. 411–414) gives rational approximations for .
7: 25.20 Approximations
§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).