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

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 …

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 …

Nov 8, 2016 · Integration of Erf function Ask Question Asked 9 years, 1 month ago Modified 9 years, 1 month ago

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.

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 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.

Nov 30, 2015 · @user2879934: yes, but the point is that the relationship between erf and erfc should give you insight into how the integral over erf diverges.