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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

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


Authors: M. M. Shepherd and J. G. Laframboise
Journal: Math. Comp. 36 (1981), 249-253
MSC: Primary 65D20
DOI: https://doi.org/10.1090/S0025-5718-1981-0595058-X
MathSciNet review: 595058
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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


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DOI: https://doi.org/10.1090/S0025-5718-1981-0595058-X
Article copyright: © Copyright 1981 American Mathematical Society