Chebyshev-series%20expansions
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1: 7.24 Approximations
Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
§7.24(ii) Expansions in Chebyshev Series
… ►Schonfelder (1978) gives coefficients of Chebyshev expansions for on , for on , and for on (30D).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
§7.24(iii) Padé-Type Expansions
…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.
Piessens and Branders (1972) gives the coefficients of the Chebyshev-series expansions of and , , for (23D).
3: 6.20 Approximations
§6.20(ii) Expansions in Chebyshev Series
… ►Luke and Wimp (1963) covers for (20D), and and for (20D).
Luke (1969b, pp. 41–42) gives Chebyshev expansions of , , and for , . The coefficients are given in terms of series of Bessel functions.
Luke (1969b, pp. 321–322) covers and for (the Chebyshev coefficients are given to 20D); for (20D), and for (15D). Coefficients for the sine and cosine integrals are given on pp. 325–327.
Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric -function (§13.2(i)) from which Chebyshev expansions near infinity for , , and follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the functions. If the scheme can be used in backward direction.