Difference between revisions of "Sinh"
From specialfunctionswiki
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[[Relationship between sinh, inverse Gudermannian, and tan]]<br /> | [[Relationship between sinh, inverse Gudermannian, and tan]]<br /> | ||
[[Period of sinh]]<br /> | [[Period of sinh]]<br /> | ||
| + | [[Sum of cosh and sinh]]<br /> | ||
=See Also= | =See Also= | ||
Revision as of 23:36, 21 October 2017
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
Sum of cosh and sinh
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.1$
