# Difference between revisions of "Sinh"

From specialfunctionswiki

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[[Sine]]<br /> | [[Sine]]<br /> | ||

[[Arcsinh]] | [[Arcsinh]] | ||

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+ | =References= | ||

+ | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Cosh}}: 4.5.1 | ||

<center>{{:Hyperbolic trigonometric functions footer}}</center> | <center>{{:Hyperbolic trigonometric functions footer}}</center> | ||

[[Category:SpecialFunction]] | [[Category:SpecialFunction]] |

## Revision as of 21:58, 21 June 2016

The hyperbolic sine function $\mathrm{sinh} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by $$\mathrm{sinh}(z)=\dfrac{e^z-e^{-z}}{2}.$$ Since this function is one-to-one, its inverse function the inverse hyperbolic sine function is clear.

Domain coloring of $\sinh$.

# Properties

Derivative of sinh

Pythagorean identity for sinh and cosh

Relationship between sinh and hypergeometric 0F1

Weierstrass factorization of sinh

Taylor series for sinh

Relationship between Bessel I sub 1/2 and sinh

Relationship between sin and sinh

Relationship between sinh and sin

Relationship between tangent, Gudermannian, and sinh

Relationship between sinh, inverse Gudermannian, and tan

# See Also

# References

- 1964: Milton Abramowitz and Irene A. Stegun:
*Handbook of mathematical functions*... (previous) ... (next): 4.5.1

**Hyperbolic trigonometric functions**