Difference between revisions of "Sinh"

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File:Sinhplot.png|Plot of $\mathrm{sinh}$ on $[-5,5]$.
File:Sinhplot.png|Graph of $\mathrm{sinh}$ on $[-5,5]$.
File:Complexsinhplot.png|[[Domain coloring]] of $\sinh$.
File:Complexsinhplot.png|[[Domain coloring]] of $\sinh$.

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.


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


<center>Hyperbolic trigonometric functions