File:Gjl-t(x).svg

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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