sine integrals
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1: 6.2 Definitions and Interrelations
2: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
… ►3: 6.1 Special Notation
4: 6.21 Software
5: 6.5 Further Interrelations
6: 6.14 Integrals
7: 6.19 Tables
§6.19(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 5) includes , , , , ; , , , , ; , , , , ; , , , , ; , , . Accuracy varies but is within the range 8S–11S.
Zhang and Jin (1996, pp. 652, 689) includes , , , 8D; , , , 8S.
8: 6.20 Approximations
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
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. 402, 410, and 415–421) gives main diagonal Padé approximations for , , (valid near the origin), and (valid for large ); approximate errors are given for a selection of -values.