# Sinh

From specialfunctionswiki

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[edit]

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

# See Also[edit]

# References[edit]

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

**Hyperbolic trigonometric functions**