Definition:Hyperbolic Cotangent/Definition 2
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Definition
The hyperbolic cotangent function is defined on the complex numbers as:
- $\coth: X \to \C$:
- $\forall z \in X: \coth z := \dfrac {\cosh z} {\sinh z}$
where:
- $\sinh$ is the hyperbolic sine
- $\cosh$ is the hyperbolic cosine
- $X = \set {z : z \in \C, \ \sinh z \ne 0}$
Also see
- Definition:Hyperbolic Sine
- Definition:Hyperbolic Cosine
- Definition:Hyperbolic Tangent
- Definition:Hyperbolic Secant
- Definition: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: $5$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbolic function