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Sech






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Elementary Functions > Sech[z] > Introduction to the Hyperbolic Secant Function





Definition of the hyperbolic secant function for a complex argument

In the complex ‐plane, the function is defined by the same formula 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 secant function over the complex plane.





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