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Tanh






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Elementary Functions > Tanh[z] > Introduction to the Hyperbolic Tangent Function





Definition of the hyperbolic tangent function for a complex argument


In the complex ‐plane, the function is defined by the same formula that is used for real values:

In the points , where has zeros, the denominator of the last formula equals zero and has singularities (poles of the first order).

Here are two graphics showing the real and imaginary parts of the hyperbolic tangent function over the complex plane.





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