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Key words and phrases. Special function approximation, error functions, Chebyshev expansions. "The symmetry of the function erf(-x) =-erf(;c) means that the function need only be approximated for positive x. Note. The notation 2J_q denotes the summation is performed with the term in r = 0 divided by 2. The Chebyshev polynomials Tr(t) are those defined on the range t 6 (-1, +1) i.e. Tr(t) = Cos[r arccos(r)]. **The notation for functions and their definitions is that used in M. ABRAMOWITZ & I.

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