Definition:Real Hyperbolic Cosecant/Definition 2
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Definition
The real hyperbolic cosecant function is defined on the real numbers as:
- $\csch: \R_{\ne 0} \to \C$:
- $\forall x \in \R_{\ne 0}: \csch x := \dfrac 1 {\sinh x}$
where $\sinh$ is the real hyperbolic sine.
It is noted that at $x = 0$ we have that $\sinh x = 0$, and so $\csch x$ is not defined at that point.
Also see
- Definition:Real Hyperbolic Sine
- Definition:Real Hyperbolic Cosine
- Definition:Real Hyperbolic Tangent
- Definition:Real Hyperbolic Cotangent
- Definition:Real Hyperbolic Secant
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $8.10$: Relationships among Hyperbolic Functions
- 1972: Frank Ayres, Jr. and J.C. Ault: Theory and Problems of Differential and Integral Calculus (SI ed.) ... (previous) ... (next): Chapter $15$: Differentiation of Hyperbolic Functions: Definition of Hyperbolic Functions
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbolic function
- Weisstein, Eric W. "Hyperbolic Cosecant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperbolicCosecant.html