complementary error function
1—10 of 46 matching pages
3: 7.3 Graphics
§7.17(iii) Asymptotic Expansion of for Small… ►
§7.22(iii) Repeated Integrals of the Complementary Error Function►The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing . … ►The computation of these functions can be based on algorithms for the complementary error function with complex argument; compare (7.19.3). …
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.
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).
Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for , , , , and ; approximate errors are given for a selection of -values.
§7.21 Physical Applications… ►Carslaw and Jaeger (1959) gives many applications and points out the importance of the repeated integrals of the complementary error function . …
10: 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.
Fettis et al. (1973) gives the first 100 zeros of and (the table on page 406 of this reference is for , not for ), 11S.