trigonometric%20functions
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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: 20.10 Integrals
§20.10 Integrals
►§20.10(i) Mellin Transforms with respect to the Lattice Parameter
… ►Here again denotes the Riemann zeta function (§25.2). … ►§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
… ►For corresponding results for argument derivatives of the theta functions see Erdélyi et al. (1954a, pp. 224–225) or Oberhettinger and Badii (1973, p. 193). …3: 36.4 Bifurcation Sets
4: 7.23 Tables
Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
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.
Fettis et al. (1973) gives the first 100 zeros of and (the table on page 406 of this reference is for , not for ), 11S.
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
6: 7.8 Inequalities
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.
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.
8: Bibliography F
9: 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.