@deepthought said
exp[-x²] is an elementary function. Elementary functions are polynomials, quotients, trigonometric functions, exponentials (including sinh, cosh and tanh), their inverses and any function that can be produced by combining them. However, the error function, giving the area under the curve of exp[-x²] up to some limit y, cannot be expressed in closed form i.e. as an eleme ...[text shortened]... kipedia has a nice demonstration of how to do it:
https://en.wikipedia.org/wiki/Gaussian_integral
Yeah, I was pointing out to Eladar that we are not using y = e^(-x^2) as the function in the way we did the logistical function.
I was saying they are using "Int[y dx}" as the starting point.
"However, the error function, giving the area under the curve of exp[-x²] up to some limit y, cannot be expressed in closed form i.e. as an elementary function. It's important in all sorts of statistical fields."
I stated this in my following reply to Eladar, where he said "That would just be the area under that curve."
I thought though his statement is true, it presents the matter of fitting Y = int [ y dx ] as trivial. I cant imagine that to be the case, but we all have different levels of triviality I suppose.