Difference between revisions of "Relationship between coth and cot"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\coth(z)=i\cot(iz),$$ | $$\coth(z)=i\cot(iz),$$ | ||
where $\coth$ denotes the [[coth|hyperbolic cotangent]] and $\cot$ denotes the [[cotangent]]. | where $\coth$ denotes the [[coth|hyperbolic cotangent]] and $\cot$ denotes the [[cotangent]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between sech and sec|next=Period of sinh}}: $4.5.12$ | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 19:38, 22 November 2016
Theorem
The following formula holds: $$\coth(z)=i\cot(iz),$$ where $\coth$ denotes the hyperbolic cotangent and $\cot$ denotes the cotangent.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.12$
