Difference between revisions of "Relationship between coth and csch"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\mathrm{coth} \left( \dfrac{z}{2} \right) - \mathrm{coth}(z) = \mathrm{csch}(z),$$ | $$\mathrm{coth} \left( \dfrac{z}{2} \right) - \mathrm{coth}(z) = \mathrm{csch}(z),$$ | ||
where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]] and $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]]. | where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]] and $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 03:54, 17 June 2016
Theorem
The following formula holds: $$\mathrm{coth} \left( \dfrac{z}{2} \right) - \mathrm{coth}(z) = \mathrm{csch}(z),$$ where $\mathrm{coth}$ denotes the hyperbolic cotangent and $\mathrm{csch}$ denotes the hyperbolic cosecant.
