Difference between revisions of "Relationship between coth and csch"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\mathrm{coth} \left( \dfrac{z}{2} \right) - \mathrm{coth}(z) = \m...") |
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| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>[[Relationship between coth and csch|Theorem]]:</strong> The following formula holds: |
$$\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),$$ | ||
where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]] and $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]]. | where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]] and $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]]. | ||
Revision as of 22:42, 30 May 2016
Theorem: The following formula holds: $$\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.
Proof: █
