sine%20integrals
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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
3: Bibliography M
4: 7.23 Tables
Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
Abramowitz and Stegun (1964, Table 27.6) includes the Goodwin–Staton integral , , 4D; also , , 4D.
Zhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of , , , 7D and 8D, respectively; the real and imaginary parts of , , , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.
Zhang and Jin (1996, p. 642) includes the first 10 zeros of , 9D; the first 25 distinct zeros of and , 8S.
5: 25.12 Polylogarithms
Integral Representation
… ►§25.12(iii) Fermi–Dirac and Bose–Einstein Integrals
►The Fermi–Dirac and Bose–Einstein integrals are defined by … ►In terms of polylogarithms …6: 20.10 Integrals
§20.10 Integrals
… ►7: 7.8 Inequalities
8: 7.24 Approximations
§7.24(i) Approximations in Terms of Elementary Functions
… ►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.