1—10 of 168 matching pages
§16.26 Approximations►For discussions of the approximation of generalized hypergeometric functions and the Meijer -function in terms of polynomials, rational functions, and Chebyshev polynomials see Luke (1975, §§5.12 - 5.13) and Luke (1977b, Chapters 1 and 9).
§31.13 Asymptotic Approximations►For asymptotic approximations for the accessory parameter eigenvalues , see Fedoryuk (1991) and Slavyanov (1996). ►For asymptotic approximations of the solutions of Heun’s equation (31.2.1) when two singularities are close together, see Lay and Slavyanov (1999). ►For asymptotic approximations of the solutions of confluent forms of Heun’s equation in the neighborhood of irregular singularities, see Komarov et al. (1976), Ronveaux (1995, Parts B,C,D,E), Bogush and Otchik (1997), Slavyanov and Veshev (1997), and Lay et al. (1998).
§10.76 Approximations… ►
§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions… ►
Bickley Functions… ►
Spherical Bessel Functions… ►
§4.47 Approximations… ►
§4.47(iii) Padé Approximations►Luke (1975, Chapter 3) supplies real and complex approximations for , , , , , , . …
§7.24(i) Approximations in Terms of Elementary Functions… ►
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).
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).