# Difference between revisions of "Sinh"

From specialfunctionswiki

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− | File:Sinhplot.png| | + | File:Sinhplot.png|Graph of $\mathrm{sinh}$ on $[-5,5]$. |

File:Complexsinhplot.png|[[Domain coloring]] of $\sinh$. | File:Complexsinhplot.png|[[Domain coloring]] of $\sinh$. | ||

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## Revision as of 06:48, 9 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

**Hyperbolic trigonometric functions**