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SIGMOID CURVE
Sigmoid : sigma shaped. 
A sigmoid curve is a curve having, not the shape of an
S,
but rather that of a stretched S. More precisely: curve located between
two parallel asymptotes having a point of inflection, which is
also center of symmetry, located equidistant from the
two asymptotes.
Examples of sigmoids normalized so that they are curves
of an odd differentiable function f increasing from –1 to 1 on the
reals and satisfying .
Function f  Comments  Outline 
Correspond to a branch of the puntiform quartic : . 


Connection of two portions of hyperbolas : . 


for t > 0.

Generalization of the two previous ones; opposite, animation for t ranging from 0.2 to 8. 

Hperbolic tangentoid 


Tangentoid. 

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© Robert FERRÉOL 2023