Difference between revisions of "Sinh"
From specialfunctionswiki
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=Properties= | =Properties= | ||
| − | + | [[Derivative of sinh]]<br /> | |
| − | + | [[Pythagorean identity for sinh and cosh]]<br /> | |
| − | + | [[Relationship between sinh and hypergeometric 0F1]]<br /> | |
| − | + | [[Weierstrass factorization of sinh]]<br /> | |
| − | + | [[Taylor series for sinh]]<br /> | |
| − | + | [[Relationship between Bessel I sub 1/2 and sinh]]<br /> | |
| − | + | [[Relationship between sin and sinh]]<br /> | |
| − | + | [[Relationship between sinh and sin]]<br /> | |
| − | + | [[Relationship between tangent, Gudermannian, and sinh]]<br /> | |
| − | + | [[Relationship between sinh, inverse Gudermannian, and tan]]<br /> | |
=See Also= | =See Also= | ||
Revision as of 07:50, 8 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.
Plot of $\mathrm{sinh}$ on $[-5,5]$.
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
