N ( Skwarnicki 1986 ) is a normalization factor and \ alpha, n, \ bar x and \ sigma are parameters which are fitted with the data . erf is the error function.
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A standard example of such a function is e ^ {-x ^ 2 }, whose antiderivative is ( with a multiplier of a constant ) the error function, familiar from statistics.
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The Error function is once way of doing this, I suspect there are others ( correct me if I am wrong ) . talk ) 04 : 23, 7 May 2008 ( UTC)
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:: : Well, the error function is just defined from that integral, so any other thing that it evaluates to is equivalent ( or a generalisation, like the hypergeometric functions ).
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In the graphs above, note that the blue error function is sometimes better than ( inside of ) the red function, but sometimes worse, meaning that it is not quite the optimal polynomial.
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When the error function is evaluated for arbitrary complex arguments " z ", the resulting "'complex error function "'is usually discussed in scaled form as the Faddeeva function:
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When the error function is evaluated for arbitrary complex arguments " z ", the resulting "'complex error function "'is usually discussed in scaled form as the Faddeeva function:
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Remez's algorithm is typically started by choosing the extrema of the Chebyshev polynomial T _ { N + 1 } as the initial points, since the final error function will be similar to that polynomial.
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In a conference paper ( July 2004 ) comparing tanh-sinh quadrature with Gaussian quadrature and error function quadrature, Bailey and Li found : " Overall, the tanh-sinh scheme appears to be the best.
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The HSE ( Heyd-Scuseria-Ernzerhof ) exchange-correlation functional uses an error function screened Coulomb potential to calculate the exchange portion of the energy in order to improve computational efficiency, especially for metallic systems.
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