exponential%20growth
(0.002 seconds)
11—20 of 469 matching pages
11: 7.8 Inequalities
12: 16.25 Methods of Computation
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).
Schonfelder (1978) gives coefficients of Chebyshev expansions for on , for on , and for on (30D).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
14: 20 Theta Functions
Chapter 20 Theta Functions
…15: 10.75 Tables
Achenbach (1986) tabulates , , , , , 20D or 18–20S.
British Association for the Advancement of Science (1937) tabulates , , , 7–8D; , , , 7–10D; , , , , , 8D. Also included are auxiliary functions to facilitate interpolation of the tables of , for small values of .
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
The main tables in Abramowitz and Stegun (1964, Chapter 9) give , , , , 8D–10D or 10S; , , , ; , , , 8D; , , , , 5S; , , , , 9–10S.
Zhang and Jin (1996, p. 271) tabulates , , , , , 8D.
16: 25.12 Polylogarithms
17: 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.
18: 2.11 Remainder Terms; Stokes Phenomenon
19: 4.11 Sums
§4.11 Sums
►For infinite series involving logarithms and/or exponentials, see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §44), and Prudnikov et al. (1986a, Chapter 5).20: 9.18 Tables
Fox (1960, Table 3) tabulates , , , and for , together with similar auxiliary functions for negative values of . Precision is 10D.
Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
Sherry (1959) tabulates , , , , ; 20S.
Zhang and Jin (1996, p. 339) tabulates , , , , , , , , ; 8D.