It is unfortunate that changes from Glaisher’s original $\mathrm {Erf}$: the switch of limits, names and the standardizing factor, did not apply to what Glaisher acknowledged was its most …

Well, there's a definition of erf and a definition of the Normal CDF.. The relations, derivable by some routine calculations, are shown as to how to convert between them, and how to convert …

The naïve (alternating) Maclaurin series is not really that numerically sound; I had already mentioned in my answer the modified series that has much better properties for computing …

Aug 27, 2014 · Looking at the graph of $\mathrm {erf}$ we find that it is symmetric about the origin, so approximations can be restricted to the positive half-plane. The graph further …

Aug 15, 2016 · I consider $\tanh { (x)}$ to be the somewhat prettyier function, and so I wanted to find an approximation to $\text {erf}$ with "nice functions" by a short expression.

Oct 26, 2023 · Here you could see it in Desmos where the maximum aplitude difference is lower than $0.0007$. Also note that don't requires to be defined as a piecewise function. Does this …

May 10, 2018 · The value of the integral starts at zero and grows toward the asymptote one. It reaches one only when z reaches infinity (so to speak, b/c/ infinity is not a number).

The inverse functions are quantile functions for Incomplete Gamma function based distributions and $\erf ^ {-1}$ is the quantile function for the Normal Distribution:

As you suspect, Taylor series expansions are only accurate near one point. To obtain a polynomial approximation that's good over an entire interval, the standard technique is to use …

Oct 4, 2017 · If the values aren't listed on the Wolfram function page, I would be surprised if you found them anywhere else. The only listed closed form values are for $0$, $\pm\infty$, and …