SigmoidFunction
SigmoidReImAbs

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

(5)
(6)

It has Maclaurin series

(7)
(8)

where E_n(x) is an Euler polynomial and B_n is a Bernoulli number.

x=0

It has an inflection point at , where

(10)

The same as the solution to the ordinary differential equation

(11)
y(0)=1/2

with initial condition .