$$ \begin{equation} f(x)=\frac{L}{1+e^{-k(x-x_0)}} \end{equation} $$
Fig 1. (img) Logistic Function
$$ \begin{equation} S(x)= \frac{1}{1+e^{-t}} \end{equation} $$
Fig 2. (img) Sigmoid Function
What are the differences between Logistic Function and Sigmoid Function? Is the logistic function a generalized kind of sigmoid function where you could have a higher maximum value?