Difference between revisions of "Relationship between tanh and tan"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\tanh(z)=-i \tan(iz),$$ whe...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\tanh(z)=-i \tan(iz),$$ | $$\tanh(z)=-i \tan(iz),$$ | ||
where $\tanh$ is the [[tanh|hyperbolic tangent]] and $\tan$ is the [[tangent]]. | where $\tanh$ is the [[tanh|hyperbolic tangent]] and $\tan$ is the [[tangent]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between cosh and cos|next=Relationship between csch and csc}}: $4.5.9$ | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 19:38, 22 November 2016
Theorem
The following formula holds: $$\tanh(z)=-i \tan(iz),$$ where $\tanh$ is the hyperbolic tangent and $\tan$ is the tangent.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.9$
