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
  
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[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 03:40, 6 July 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.

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

Sine
Arcsinh

References

Hyperbolic trigonometric functions