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Which should result in a function normalised to the interval $[-1,1)$ ??? what needs doing to make this. This is something like a simple auto-correlation function although only in concept, it's properties will be quite different. The function should higlight the 'area centre' of some function, such that the area on the left side is that on the right side. For a given function with an 'area centre' of 0, the function may mor may not be symetric about the y axis. For simple functions the derivative of the fold function equal to zero will yeild a location for this cetre point.  Porbably more realistic to scale down the $\infty$ to some large value for terminating functions etc. numeric analysis. Moved on to study the transform \begin{equation}  F(x)=2*f_{max}[ \frac{ \int_{x}^{\infty} f(s) \;ds}{ \int_{-\infty}^{x} f(s) \;ds} +   \frac{ \int_{-\infty}^{x} f(s) \;ds}{ \int_{x}^{\infty} f(s) \;ds}]  \end{equation}