Chebyshev approximation of $(1+2x) \textrm {exp}(x^{2}) \textrm {erfc} x$ in $0\leq x<\infty$

Abstract:

We have obtained a single Chebyshev expansion of the function $f(x) = (1 + 2x)\exp ({x^2}){\text {erfc}} x$ in $0 \leqslant x < \infty$, accurate to 22 decimal digits. The presence of the factors $(1 + 2x)\exp ({x^2})$ causes $f(x)$ to be of order unity throughout this range, ensuring that the use of $f(x)$ for approximating erfc x will give uniform relative accuracy for all values of x