# Sigmoid function (chart) Calculator

## Calculates a table of the sigmoid functions (sa(x), s'a(x) and s''a(x)) and draws the chart.

 The sigmoid function is used in the activation function of the neural network.
 a(gain) initial value x [increment repetition ]
 $\normal Sigmoid\ function\ \varsigma_{\alpha}(x)\\[10]\varsigma_{\alpha}(x) = \large \frac{1}{1+e^{-\alpha x}} = \large \frac {\tanh(\alpha x /2) + 1}{2}\\[15]\normal \varsigma '_{\alpha}(x) = \alpha \varsigma_{\alpha}(x) \{ 1 - \varsigma_{\alpha}(x) \} \\[15]\normal \varsigma ''_{\alpha}(x) = \alpha^{2} \varsigma_{\alpha}(x) \{ 1- \varsigma_{\alpha}(x) \} \{ 1 - 2 \varsigma_{\alpha}(x) \} \\[15]$

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