Sigmoid Function

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Sigmoid Function

2024-07-10 09:23| 来源: 网络整理| 查看: 265

Sigmoid Function Download Wolfram Notebook

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 .

See alsoEinstein Functions, Exponential Function, Exponential Ramp, Heaviside Step Function, Logistic Distribution, Logistic Equation Explore with Wolfram|Alpha

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sigmoid function plot sigmoid function x from -10 to 10 graph sigmoid function from -5 to 5 Referencesvon Seggern, D. CRC Standard Curves and Surfaces with Mathematics, 2nd ed. Boca Raton, FL: CRC Press, 2007.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

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Sigmoid Function

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