Definition:Inverse Hyperbolic Secant/Complex/Principal Branch

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

 * Derivation of Area Hyperbolic Secant from Inverse Hyperbolic Secant Multifunction


 * 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