Definition:Hyperbolic Cosine/Real

Definition

The real hyperbolic cosine function is defined on the real numbers as:

$\cosh: \R \to \R$:

$\forall x \in \R: \cosh x := \dfrac {e^x + e^{-x} } 2$

Also see

• Definition:Real Hyperbolic Sine
• Definition:Real Hyperbolic Tangent
• Definition:Real Hyperbolic Cotangent
• Definition:Real Hyperbolic Secant
• Definition:Real Hyperbolic Cosecant

• Equation of Catenary

• Results about the hyperbolic cosine function can be found here.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $8.2$: Definition of 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
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.11$: The Catenary, or Curve of a Hanging Chain: Footnote $1$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbolic function

• Weisstein, Eric W. "Hyperbolic Cosine." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperbolicCosine.html