Answer by Claude Leibovici for Approximating for the Error function...
In my first answer, I tried to stay as close as possible to your initial attempf.Restarting from scratch, what we have is$$\tanh ^{-1}(\text{erf}(x))=t\sum_{n=0}^\infty a_n\,t^{2n} \qquad...
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Answer by heropup for Approximating for the Error function $\text{erf}(x)$...
The approximation is bad because the tails are totally different.The standard normal density is proportional to $e^{-x^2}$. The hyperbolic tangent, whose derivative is the square of the hyperbolic...
View ArticleAnswer by Claude Leibovici for Approximating for the Error function...
Your idea is good but I think that we can do a bit better using it.Starting from scratch, if you want to write$$\text{erf}(x)\sim\tanh \left(\frac{a x}{b+c x+d x^2}\right)$$ use a series expansion...
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Approximating for the Error function $\text{erf}(x)$ through an Hyperbolic...
Approximating for the Error function$\text{erf}(x)$ through an Hyperbolic tangent function$\text{tanh}\left(\dfrac{4x}{4-x^2}\right)$I was plotting some functions and I found that the function$$f(x) =...
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