Definition:Inverse Hyperbolic Cosine/Complex/Principal Branch
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Definition
The principal branch of the complex inverse hyperbolic cosine function is defined as:
- $\forall z \in \C: \map \Arcosh z := \map \Ln {z + \sqrt {z^2 - 1} }$
where:
- $\Ln$ denotes the principal branch of the complex natural logarithm
- $\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.
Also see
- Definition:Complex Area Hyperbolic Sine
- Definition:Complex Area Hyperbolic Tangent
- Definition:Complex Area Hyperbolic Cotangent
- Definition:Complex Area Hyperbolic Secant
- Definition:Complex Area Hyperbolic Cosecant
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $8$