error%20control
(0.002 seconds)
1—10 of 240 matching pages
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: 7.2 Definitions
§7.2(i) Error Functions
… ►Values at Infinity
►3: 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.
4: 7.23 Tables
Zhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
Abramowitz and Stegun (1964, Chapter 7) includes , , , 6D.
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.