On Sun, 12 Sep 2010, Martin Peach wrote:
plot [-2:2] [-1:1] exp(x*sqrt(2))-1, 1-exp(-x*sqrt(2)), tanh(x), x
Of course, all the hyperbolic trig functions are made from exp, by definition.
Ah, some other things I wanted to say :
Even though tanh is made from exp, it's not directly the same as the two simpler exponentials (above) that may describe capacitor behaviour more directly. What I wanted to show is tanh is a rather good approximation to both at once, but only if you put an extra sqrt(2) factor.
And to finish about the sigmoïd, tanh(x) is usually written as (exp(x)-exp(-x))/(exp(x)+exp(-x)), but you can also write it as 1-2/(1+exp(2*x)), which is almost the usual form of the sigmoïd function.
| Mathieu Bouchard ------------------------------ Villeray, Montréal, QC