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) =...
Opengraph URL: https://mathworld.wolfram.com/SigmoidFunction.html
Domain: mathworld.wolfram.com
| DC.Title | Sigmoid Function |
| DC.Creator | Weisstein, 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.Modified | 2008-12-26 |
| DC.Subject | 33B10 |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/SigmoidFunction.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2008-12-26 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_SigmoidFunction.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_SigmoidFunction.png |
| None | ie=edge |
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