tanh
Represents the hyperbolic tangent function, a fundamental mathematical function that maps real numbers to values between -1 and 1.
Overview
Essential in various mathematical and scientific applications, particularly in neural networks, signal processing, and differential equations.
- Commonly used in machine learning as an activation function due to its smooth, bounded output range
- Appears frequently in physics for describing wave mechanics and electromagnetic phenomena
- Important in engineering applications involving damped oscillations and control systems
- Serves as a key function in complex analysis and differential geometry
Examples
Hyperbolic tangent function in a basic mathematical expression
\tanh(x) = \frac{\sinh(x)}{\cosh(x)}Neural network activation function with specific input
f(x) = \tanh(wx + b)Solution to a differential equation involving hyperbolic tangent
y(t) = A\tanh(\omega t)