Difference between revisions of "Csch"
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[[Derivative of hyperbolic cosecant]]<br /> | [[Derivative of hyperbolic cosecant]]<br /> | ||
[[Antiderivative of hyperbolic cosecant]]<br /> | [[Antiderivative of hyperbolic cosecant]]<br /> | ||
| + | [[Relationship between csch and csc]]<br /> | ||
[[Relationship between cot, Gudermannian, and csch]]<br /> | [[Relationship between cot, Gudermannian, and csch]]<br /> | ||
[[Relationship between csch, inverse Gudermannian, and cot]]<br /> | [[Relationship between csch, inverse Gudermannian, and cot]]<br /> | ||
Revision as of 22:05, 21 June 2016
The hyperbolic cosecant function $\mathrm{csch} \colon \mathbb{R} \setminus \{0\} \rightarrow \mathbb{R} \setminus \{0\}$ is defined by $$\mathrm{csch}(z)=\dfrac{1}{\sinh(z)},$$ where $\sinh$ denotes the hyperbolic sine. Since this function is one-to-one, its inverse function, the inverse hyperbolic cosecant function is clear.
Plot of $\mathrm{csch}$ on $[-5,5]$.
Domain coloring of analytic continuation of $\mathrm{csch}$.
Properties
Derivative of hyperbolic cosecant
Antiderivative of hyperbolic cosecant
Relationship between csch and csc
Relationship between cot, Gudermannian, and csch
Relationship between csch, inverse Gudermannian, and cot
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.5.3
