Definition:Inverse Hyperbolic Secant/Complex/Principal Branch
< Definition:Inverse Hyperbolic Secant | Complex(Redirected from Definition:Complex Area Hyperbolic Secant)
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Definition
The principal branch of the complex inverse hyperbolic secant function is defined as:
- $\forall z \in \C: \map \Arsech z := \map \Ln {\dfrac {1 + \sqrt {1 - z^2} } z}$
where:
- $\Ln$ denotes the principal branch of the complex natural logarithm
- $\sqrt {1 - z^2}$ denotes the principal square root of $1 - z^2$.
Also see
- Definition:Complex Area Hyperbolic Sine
- Definition:Complex Area Hyperbolic Cosine
- Definition:Complex Area Hyperbolic Tangent
- Definition:Complex Area Hyperbolic Cotangent
- 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: $8$