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Chebyshev Approximation of $(1 + 2x)\exp(x^2)\operatorname{erfc} x$ in $0 \leqslant x < \infty$

M. M. Shepherd and J. G. Laframboise
Mathematics of Computation
Vol. 36, No. 153 (Jan., 1981), pp. 249-253
DOI: 10.2307/2007742
Stable URL: http://www.jstor.org/stable/2007742
Page Count: 5
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Chebyshev Approximation of $(1 + 2x)\exp(x^2)\operatorname{erfc} x$ in $0 \leqslant x < \infty$
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Abstract

We have obtained a single Chebyshev expansion of the function $f(x) = (1 + 2x)\exp(x^2)\operatorname{erfc} x$ 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 $\operatorname{erfc} x$ will give uniform relative accuracy for all values of $x$.

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