sine and cosine integrals
1—10 of 151 matching pages
§8.21 Generalized Sine and Cosine Integrals… ►From here on it is assumed that unless indicated otherwise the functions , , , and have their principal values. … ►
§8.21(v) Special Values… ►For the corresponding expansions for and apply (8.21.20) and (8.21.21).
§6.2(ii) Sine and Cosine Integrals… ►
Hyperbolic Analogs of the Sine and Cosine Integrals… ►
§6.5 Further Interrelations… ►
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.
8: 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.