Difference between revisions of "Cosh"

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The hyperbolic cosine function $\cosh \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
 
The hyperbolic cosine function $\cosh \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
$$\mathrm{cosh}(z)=\dfrac{e^z + e^{-z}}{2}$$
+
$$\mathrm{cosh}(z)=\dfrac{e^z + e^{-z}}{2}.$$
  
 
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[[Cosh is even]]<br />
 
[[Cosh is even]]<br />
 
[[Sinh of a sum]]<br />
 
[[Sinh of a sum]]<br />
 +
[[Cosh of a sum]]<br />
 +
[[Halving identity for sinh]]<br />
 +
[[Halving identity for cosh]]<br />
 +
[[Halving identity for tangent (1)]]<br />
 +
[[Halving identity for tangent (2)]]<br />
 +
[[Halving identity for tangent (3)]]<br />
 +
[[Doubling identity for sinh (1)]]<br />
 +
[[Doubling identity for cosh (1)]]<br />
 +
[[Doubling identity for cosh (2)]]<br />
 +
[[Doubling identity for cosh (3)]]<br />
  
 
=See Also=
 
=See Also=

Latest revision as of 23:44, 21 October 2017


The hyperbolic cosine function $\cosh \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{cosh}(z)=\dfrac{e^z + e^{-z}}{2}.$$

Properties

Derivative of cosh
Pythagorean identity for sinh and cosh
Weierstrass factorization of cosh
Relationship between cosh and hypergeometric 0F1
Relationship between Bessel I sub 1/2 and cosh
Relationship between cosh and cos
Relationship between cos and cosh
Relationship between secant, Gudermannian, and cosh
Relationship between cosh, inverse Gudermannian, and sec
Period of cosh
Sum of cosh and sinh
Difference of cosh and sinh
Cosh is even
Sinh of a sum
Cosh of a sum
Halving identity for sinh
Halving identity for cosh
Halving identity for tangent (1)
Halving identity for tangent (2)
Halving identity for tangent (3)
Doubling identity for sinh (1)
Doubling identity for cosh (1)
Doubling identity for cosh (2)
Doubling identity for cosh (3)

See Also

Arccosh

References

Hyperbolic trigonometric functions