th

By way of analogy with the usual tangent tan z congruent (sin z)/(cos z), the hyperbolic tangent is defined as tanh z | congruent | (sinh z)/(cosh z) | = | (e^z - e^(-z))/(e^z + e^(-z)) | = | (e^(2z) - 1)/(e^(2z) + 1), where sinh z is the hyperbolic sine and cosh z is the hyperbolic cosine. The notation th z is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix).

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Tanh