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Title: Sigmoid Function -- from Wolfram MathWorld

Open Graph Title: Sigmoid Function -- from Wolfram MathWorld

X Title: Sigmoid Function -- from Wolfram MathWorld

Description: The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = [1-y(x)]y(x) (2) = (e^(-x))/((1+e^(-x))^2) (3) = (e^x)/((1+e^x)^2) (4) and indefinite integral intydx = x+ln(1+e^(-x)) (5) = ln(1+e^x). (6) It has Maclaurin series y(x) = sum_(n=0)^(infty)((-1)^nE_n(0))/(2n!)x^n (7) = sum_(n=0)^(infty)((-1)^(n+1)(2^(n+1)-1)B_(n+1))/((n+1))x^n (8) =...

Open Graph Description: The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = [1-y(x)]y(x) (2) = (e^(-x))/((1+e^(-x))^2) (3) = (e^x)/((1+e^x)^2) (4) and indefinite integral intydx = x+ln(1+e^(-x)) (5) = ln(1+e^x). (6) It has Maclaurin series y(x) = sum_(n=0)^(infty)((-1)^nE_n(0))/(2n!)x^n (7) = sum_(n=0)^(infty)((-1)^(n+1)(2^(n+1)-1)B_(n+1))/((n+1))x^n (8) =...

X Description: The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = [1-y(x)]y(x) (2) = (e^(-x))/((1+e^(-x))^2) (3) = (e^x)/((1+e^x)^2) (4) and indefinite integral intydx = x+ln(1+e^(-x)) (5) = ln(1+e^x). (6) It has Maclaurin series y(x) = sum_(n=0)^(infty)((-1)^nE_n(0))/(2n!)x^n (7) = sum_(n=0)^(infty)((-1)^(n+1)(2^(n+1)-1)B_(n+1))/((n+1))x^n (8) =...

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DC.TitleSigmoid Function
DC.CreatorWeisstein, Eric W.
DC.Description The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = [1-y(x)]y(x) (2) = (e^(-x))/((1+e^(-x))^2) (3) = (e^x)/((1+e^x)^2) (4) and indefinite integral intydx = x+ln(1+e^(-x)) (5) = ln(1+e^x). (6) It has Maclaurin series y(x) = sum_(n=0)^(infty)((-1)^nE_n(0))/(2n!)x^n (7) = sum_(n=0)^(infty)((-1)^(n+1)(2^(n+1)-1)B_(n+1))/((n+1))x^n (8) =...
DC.Date.Modified2008-12-26
DC.Subject33B10
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/SigmoidFunction.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
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DC.TypeText
Last-Modified2008-12-26
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