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 important …

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 $\mathrm {erf} (x)$ …

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 between …

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 suggest two basic …

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.

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

Oct 26, 2023 · Here I left the plots in Desmos: Added later (after some answers) After 2 interesting answers, I got the idea of testing the series expansion of tanh−1(erf(x)) tanh 1 (erf (x)) shown in …

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).

1 Context for using the Taylor Series of $$e^ {-t^2}$$ to find the Taylor expansion of the ERF function is found at Robert Ghrist/UPenn's Calculus wiki.

Sep 24, 2022 · Please don't call your function erf.The function erf has a standard definition, which you have just quoted. Call your function Erf (k,v,z) and do a simple change of variable to relate it to erf.