Definition:Real Hyperbolic Tangent/Definition 2
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Definition
The real hyperbolic tangent function is defined on the real numbers as:
- $\tanh: \R \to \R$:
- $\forall x \in \R: \tanh x := \dfrac {\sinh x} {\cosh x}$
where:
- $\sinh$ is the real hyperbolic sine
- $\cosh$ is the real hyperbolic cosine
Also see
- Definition:Real Hyperbolic Sine
- Definition:Real Hyperbolic Cosine
- Definition:Real Hyperbolic Cotangent
- Definition:Real Hyperbolic Secant
- Definition:Real Hyperbolic Cosecant
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $8.7$: 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 Tangent." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperbolicTangent.html