relations%20to%20Dawson%20integral%20and%20exponential%20integral
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11—20 of 620 matching pages
11: 8.26 Tables
Khamis (1965) tabulates for , to 10D.
§8.26(iv) Generalized Exponential Integral
►Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
12: 20 Theta Functions
Chapter 20 Theta Functions
…13: 7.24 Approximations
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, pp. 323–324) covers and for (the Chebyshev coefficients are given to 20D); and for (the Chebyshev coefficients are given to 20D and 15D, respectively). Coefficients for the Fresnel integrals are given on pp. 328–330 (20D).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
14: William P. Reinhardt
15: 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 …16: Gergő Nemes
17: Wolter Groenevelt
18: 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.
19: 6.20 Approximations
Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
Luke (1969b, pp. 321–322) covers and for (the Chebyshev coefficients are given to 20D); for (20D), and for (15D). Coefficients for the sine and cosine integrals are given on pp. 325–327.