Difference between revisions of "Relationship between csc, Gudermannian, and coth"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\csc(\mathrm{gd}(x))=\mathrm{coth}(x),$$ where $\csc$ is the co...") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | ==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== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:43, 8 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.
