Sigmoid Function

Min Max Re Im

The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function

(1)

It has derivative

			(2)
			(3)
			(4)

and indefinite integral

			(5)
			(6)

It has Maclaurin series

			(7)
			(8)
			(9)

where is an Euler polynomial and is a Bernoulli number.

It has an inflection point at , where

(10)

It is also the solution to the ordinary differential equation

(11)

with initial condition .