Rational Chebyshev approximations for the inverse of the error function

Abstract

This report presents near-minimax rational approximations for the inverse of the error function inverf x , for 0 ⩽ x ⩽ 1 − 10 − 10000 0 \leqslant x \leqslant 1 - {10^{ - 10000}} , with relative errors ranging down to 10 − 23 {10^{ - 23}} . An asymptotic formula for the region x → 1 x \to 1 is also given.