The sigmoid function, or the sigmoidal curve (von Seggern 2007, p. 148) as well as logistic function, is the function:
It has derivative
and indefinite integral
It has Maclaurin series
where E_n(x) is an Euler polynomial and B_n is a Bernoulli number.
It has an inflection point at , where
The same as the solution to the ordinary differential equation
with initial condition .