# Difference between revisions of "Sinh"

From specialfunctionswiki

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[[Relationship between sinh, inverse Gudermannian, and tan]]<br /> | [[Relationship between sinh, inverse Gudermannian, and tan]]<br /> | ||

[[Period of sinh]]<br /> | [[Period of sinh]]<br /> | ||

+ | [[Sum of cosh and sinh]]<br /> | ||

=See Also= | =See Also= |

## Revision as of 23:36, 21 October 2017

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

Period of sinh

Sum of cosh and sinh

# See Also

# References

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

**Hyperbolic trigonometric functions**