auxiliary%20functions%20for%20sine%20and%20cosine%20integrals
(0.005 seconds)
4 matching pages
1: 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.
2: 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.
Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of , , , 6D; , , , 6D; , , , 6D.
Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of , , , 8S.
3: 7.24 Approximations
§7.24(i) Approximations in Terms of Elementary Functions
►Hastings (1955) gives several minimax polynomial and rational approximations for , and the auxiliary functions and .
Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for , , , , and ; approximate errors are given for a selection of -values.