Rational Chebyshev approximations for the error function

Abstract

This note presents nearly-best rational approximations for the functions erf ( x ) (x) and erfc ( x ) (x) , with maximal relative errors ranging down to between 6 × 10 − 19 6 \times {10^{ - 19}} and 3 × 10 − 20 3 \times {10^{ - 20}} .