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§4.47(i) Chebyshev-Series Expansions…
§12.20 Approximations►Luke (1969b, pp. 25 and 35) gives Chebyshev-series expansions for the confluent hypergeometric functions and (§13.2(i)) whose regions of validity include intervals with endpoints and , respectively. As special cases of these results a Chebyshev-series expansion for valid when follows from (12.7.14), and Chebyshev-series expansions for and valid when follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). …
§6.20(ii) Expansions in Chebyshev Series►
Clenshaw (1962) gives Chebyshev coefficients for for and for (20D).
Luke and Wimp (1963) covers for (20D), and and for (20D).
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.
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).
§5.23(ii) Expansions in Chebyshev Series►Luke (1969b) gives the coefficients to 20D for the Chebyshev-series expansions of , , , , , and the first six derivatives of for . …Clenshaw (1962) also gives 20D Chebyshev-series coefficients for and its reciprocal for . …
Luke (1975, p. 103) gives Chebyshev-series expansions for and related functions for .
§9.19(ii) Expansions in Chebyshev Series… ►
MacLeod (1994) supplies Chebyshev-series expansions to cover for and for . The Chebyshev coefficients are given to 20D.
§11.15(i) Expansions in Chebyshev Series►
Luke (1975, pp. 416–421) gives Chebyshev-series expansions for , , , and , , for ; , , , and , , ; the coefficients are to 20D.
MacLeod (1993) gives Chebyshev-series expansions for , , , and , , ; the coefficients are to 20D.