Difference between revisions of "Sinh"
From specialfunctionswiki
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[[Sine]]<br /> | [[Sine]]<br /> | ||
[[Arcsinh]] | [[Arcsinh]] | ||
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| + | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Cosh}}: 4.5.1 | ||
<center>{{:Hyperbolic trigonometric functions footer}}</center> | <center>{{:Hyperbolic trigonometric functions footer}}</center> | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 21:58, 21 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.
Graph 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
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.5.1
