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Alternate names

Definition

The inverse hyperbolic functions, sometimes also called the area hyperbolic functions are the multivalued function that are the inverse functions of the hyperbolic functions. They are denoted cosh^(-1) z, coth^(-1) z, csch^(-1) z, sech^(-1) z, sinh^(-1) z, and tanh^(-1) z. Variants of these notations beginning with a capital letter are commonly used to denote their principal values. These functions are multivalued, and hence require branch cuts in the complex plane. Differing branch cut conventions are possible, but those adopted in this work follow those used by the Wolfram Language, summarized below.