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5: 7.4 Symmetry
§7.24(i) Approximations in Terms of Elementary Functions►
Hastings (1955) gives several minimax polynomial and rational approximations for , and the auxiliary functions and .
Bulirsch (1967) provides Chebyshev coefficients for the auxiliary functions and for (15D).
§7.22(i) Main Functions…
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
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.