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1: 20 Theta Functions
Chapter 20 Theta Functions
…2: 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
… ►§6.20(iii) Padé-Type and Rational Expansions
…3: 6.16 Mathematical Applications
4: 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
… ►Schonfelder (1978) gives coefficients of Chebyshev expansions for on , for on , and for on (30D).
§7.24(iii) Padé-Type Expansions
…5: 10.75 Tables
Olver (1960) tabulates , , , , , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as ; see §10.21(viii), and more fully Olver (1954).
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Kerimov and Skorokhodov (1984c) tabulates all zeros of and in the sector for , 9S.
Olver (1960) tabulates , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as .
6: 28.16 Asymptotic Expansions for Large
7: Bibliography K
8: 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).