Difference between revisions of "Sinh"

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=Properties=
 
=Properties=
{{:Derivative of sinh}}
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[[Derivative of sinh]]<br />
{{:Pythagorean identity for sinh and cosh}}
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[[Pythagorean identity for sinh and cosh]]<br />
{{:Relationship between sinh and hypergeometric 0F1}}
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[[Relationship between sinh and hypergeometric 0F1]]<br />
{{:Weierstrass factorization of sinh}}
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[[Weierstrass factorization of sinh]]<br />
{{:Taylor series for sinh}}
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[[Taylor series for sinh]]<br />
{{:Relationship between Bessel I sub 1/2 and sinh}}
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[[Relationship between Bessel I sub 1/2 and sinh]]<br />
{{:Relationship between sin and sinh}}
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[[Relationship between sin and sinh]]<br />
{{:Relationship between sinh and sin}}
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[[Relationship between sinh and sin]]<br />
{{:Relationship between tangent, Gudermannian, and sinh}}
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[[Relationship between tangent, Gudermannian, and sinh]]<br />
{{:Relationship between sinh, inverse Gudermannian, and tan}}
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[[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.

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

<center>Hyperbolic trigonometric functions
</center>