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Sigmoid Function

\begin{figure}\begin{center}\BoxedEPSF{SigmoidFunction.epsf scaled 700}\end{center}\end{figure}

\begin{figure}\begin{center}\BoxedEPSF{SigmoidFunctionReIm.epsf scaled 800}\end{center}\end{figure}

The function

y={1\over 1+e^{-x}}

which is the solution to the Ordinary Differential Equation

{dy\over dx}=y(1-y).

It has an inflection point at $x=0$, where


See also Exponential Function, Exponential Ramp


von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 124, 1993.

© 1996-9 Eric W. Weisstein