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1: 7.18 Repeated Integrals of the Complementary Error Function
§7.18 Repeated Integrals of the Complementary Error Function
►§7.18(i) Definition
… ►§7.18(iii) Properties
… ► … ►Hermite Polynomials
…2: 7.8 Inequalities
§7.8 Inequalities
►Let denote Mills’ ratio: … ►3: 20 Theta Functions
Chapter 20 Theta Functions
…4: Bibliography G
5: 7.24 Approximations
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).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for , , , , and ; approximate errors are given for a selection of -values.
6: 22.3 Graphics
§22.3(i) Real Variables: Line Graphs
… ►§22.3(iii) Complex ; Real
►In the graphics shown in this subsection height corresponds to the absolute value of the function and color to the phase. … ►§22.3(iv) Complex
… ►In Figures 22.3.24 and 22.3.25, height corresponds to the absolute value of the function and color to the phase. …7: 8 Incomplete Gamma and Related
Functions
Chapter 8 Incomplete Gamma and Related Functions
…8: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
…9: 8.26 Tables
§8.26(ii) Incomplete Gamma Functions
►Khamis (1965) tabulates for , to 10D.
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.