auxiliary functions for sine and cosine integrals
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1: 6.1 Special Notation
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2: 6.4 Analytic Continuation
3: 6.2 Definitions and Interrelations
4: 6.11 Relations to Other Functions
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6.11.3
5: 6.20 Approximations
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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.
6: 6.5 Further Interrelations
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6.5.7
7: 6.19 Tables
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