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Summary

Description
English: Some sigmoid functions compared.

All functions are normalized in such a way that they satisfy

  • −1 < ƒ(x) < 1
  • ƒ(−x) = −ƒ(x) and hence ƒ(0) = 0
  • 0 < ƒ'(x) ≤ 1 and ƒ'(x) = 1 iff x = 0
  • ƒ(∞) = 1 and ƒ(−∞) = −1
  • all functions are analytic except x/(1+|x|) which is not analytic at 0.

For notations see also

An "interactive" plot can be generated via WolframAlpha
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This vector image includes elements that have been taken or adapted from this file:
 Error function.svg (by Geek3).
Author Georg-Johann
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15 September 2010

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Date/TimeThumbnailDimensionsUserComment
current22:40, 15 September 2010Thumbnail for version as of 22:40, 15 September 2010700 × 350 (36 KB)Georg-JohannAdd erf(x)
21:08, 15 September 2010Thumbnail for version as of 21:08, 15 September 2010700 × 350 (31 KB)Georg-Johann{{Information |Description={{en|1=will follow}} |Source={{own}} |Author=Georg-Johann |Date=2010-09-15 |Permission= |other_versions=File:Gjl-t(x).png }} Category:SVG x-y functions

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