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

Chebyshev approximation of (1+2𝑥)𝑒𝑥𝑝(𝑥²)𝑒𝑟𝑓𝑐𝑥 in 0≤𝑥<∞