Chebyshev approximations for Dawson’s integral

Abstract

Rational Chebyshev approximations to Dawson’s integral are presented in well-conditioned forms for | x | ≦ 2.5 , 2.5 ≦ | x | ≦ 3.5 , 3.5 ≦ | x | ≦ 5.0 |x| \leqq 2.5, 2.5 \leqq |x| \leqq 3.5, 3.5 \leqq |x| \leqq 5.0 and 5.0 ≦ | x | 5.0 \leqq |x| . Maximal relative errors range down to between 2 × 10 − 20 2 \times {10^{ - 20}} and 7 × 10 − 22 7 \times {10^{ - 22}} .