Difference between revisions of "Sinh"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Cosh}}: 4.5.1 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Cosh}}: $4.5.1$ |
{{:Hyperbolic trigonometric functions footer}} | {{:Hyperbolic trigonometric functions footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 19:37, 22 November 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
Period of sinh
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.1$
