What is statistics? – The Gauss Error Function

Error Function: Theoretical Definition
The Gaussian Error Function which is symbolized as erf[\latex] is very similar to <strong>Normal Distribution Function</strong> [latex]\Phi  \left ( x \right )[\latex], because it is closely related to that function. However, some terms of these functions, as they are used today, have been differentiated. Therefore, it is useful  to present such differences because both functions are essential to many scientific fields. Note that you may confront many different forms of both forms. we will present some basic forms of <strong>Error Function</strong>.   It can describe diffusion and it has a sigmoid shape. Diffusion is related to the way that particles interact when they are highly concentrated in one area, and between another area that are in low concentration.   <font color="#4B0082">Error Function: Statistical Definition</font> Statistically, it can be defined as the integral of e raised to minus squared [latex]t[latex], that must be integrated from [latex]X to 0, and then multiplied with the fraction of \frac{2}{\sqrt{\pi}}[latex], in detail, [latex]erf\left (x  \right ) is defined as:

erf\left (x  \right )=\frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-t^{2}}dt

\pi is a very useful constant that is equal to 3.1416
t is an x quantity

Error Function: Solutions and Problems
Some integrals, and therefore, The Error Function IS IMPOSSIBLE to be solved / integrated with

—Any “Elementary Function”