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Sigmoid Function

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

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(1)

It has derivative

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(2)
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and indefinite integral

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(5)
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It has Maclaurin series

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(7)
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where spacer is an Euler polynomial and spacer is a Bernoulli number.

It has an inflection point at spacer , where

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(10)

It is also the solution to the ordinary differential equation

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(11)

with initial condition spacer .

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