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.
Clenshaw (1962) gives Chebyshev coefficients for
for 
and 
for
(20D).
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.
, 
, and the
auxiliary functions 
and 
. These are included
in Abramowitz and Stegun (
, 
, 
(valid near the origin), and 
); approximate
errors are given for a selection of 
-values.