The hyperbolic tangent function, denoted as tanh, is a mathematical function that represents the ratio of the hyperbolic sine to the hyperbolic cosine. It is defined as $$tanh(x) = \frac{sinh(x)}{cosh(x)}$$. This function is commonly used in various applications, particularly in calculus and complex analysis, as it models growth processes and is crucial for understanding other hyperbolic functions and their relationships to trigonometric functions.
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