Definition:Inverse Hyperbolic Cotangent/Complex/Principal Branch

Definition

The principal branch of the complex inverse hyperbolic cotangent function is defined as:

$\forall z \in \C: \map \Arcoth z := \dfrac 1 2 \map \Ln {\dfrac {z + 1} {z - 1} }$

where $\Ln$ denotes the principal branch of the complex natural logarithm.

Also see

• Derivation of Area Hyperbolic Cotangent from Inverse Hyperbolic Cotangent Multifunction

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $8$