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BikramKumar (talk | contribs) →Analytic approximations: Directed the link of "Sigmoid Function" to the "Examples" section. Tags: Mobile edit Mobile web edit |
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<math display="block">H(x)=\lim_{k \to \infty}\tfrac{1}{2}(1+\tanh kx)=\lim_{k \to \infty}\frac{1}{1+e^{-2kx}}.</math>
There are [[Sigmoid function#Examples|many other smooth, analytic approximations]] to the step function.<ref>{{MathWorld | urlname=HeavisideStepFunction | title=Heaviside Step Function}}</ref> Among the possibilities are:
<math display="block">\begin{align}
H(x) &= \lim_{k \to \infty} \left(\tfrac{1}{2} + \tfrac{1}{\pi}\arctan kx\right)\\
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