Definition:Hyperbolic Cotangent/Definition 4
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Definition
The hyperbolic cotangent function is defined on the complex numbers as:
- $\coth: X \to \C$:
- $\forall z \in X: \coth z := \dfrac 1 {\tanh z}$
where:
- $\tanh$ is the hyperbolic tangent
- $X = \set {z : z \in \C, \ \sinh z \ne 0}$
- where $\sinh$ is the hyperbolic sine.
Also see
- Definition:Hyperbolic Sine
- Definition:Hyperbolic Cosine
- Definition:Hyperbolic Tangent
- Definition:Hyperbolic Secant
- Definition:Hyperbolic Cosecant
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hyperbolic function