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Date: 15-5-2018
1987
Date: 18-8-2018
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Date: 10-6-2019
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The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function
(1) |
It has derivative
(2) |
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(4) |
and indefinite integral
(5) |
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(6) |
It has Maclaurin series
(7) |
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(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 .
REFERENCES:
von Seggern, D. CRC Standard Curves and Surfaces with Mathematics, 2nd ed. Boca Raton, FL: CRC Press, 2007.
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