Difference between revisions of "Relationship between csc, Gudermannian, and coth"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ | $$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ | ||
where $\csc$ is the [[cosecant]], $\mathrm{gd}$ is the [[Gudermannian]], and $\mathrm{coth}$ is the [[coth|hyperbolic cotangent]]. | where $\csc$ is the [[cosecant]], $\mathrm{gd}$ is the [[Gudermannian]], and $\mathrm{coth}$ is the [[coth|hyperbolic cotangent]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 04:36, 6 June 2016
Theorem
The following formula holds: $$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ where $\csc$ is the cosecant, $\mathrm{gd}$ is the Gudermannian, and $\mathrm{coth}$ is the hyperbolic cotangent.
