The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function
It has derivative
and indefinite integral
It has Maclaurin series
is an Euler polynomial and is a Bernoulli number.
It has an inflection point at , where
It is also the solution to the ordinary
with initial condition .
See alsoEinstein Functions
, Exponential Function
, Exponential Ramp
, Logistic Distribution
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Referencesvon Seggern, D. CRC Standard Curves and Surfaces with Mathematics, 2nd ed. Boca Raton, FL: CRC
Referenced on Wolfram|AlphaSigmoid Function
Cite this as:
Weisstein, Eric W. "Sigmoid Function."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SigmoidFunction.html