Difference between revisions of "Relationship between csch and csc"
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The following formula holds: | The following formula holds: | ||
$$\mathrm{csch}(z)=i \csc(iz),$$ | $$\mathrm{csch}(z)=i \csc(iz),$$ | ||
| − | where $\csch$ denotes the [[csch|hyperbolic cosecant]] and $\csc$ denotes the [[cosecant]]. | + | where $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]] and $\csc$ denotes the [[cosecant]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between tanh and tan|next=Relationship between sech and sec}}: 4.5.10 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Relationship between tanh and tan|next=Relationship between sech and sec}}: $4.5.10$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 19:38, 22 November 2016
Theorem
The following formula holds: $$\mathrm{csch}(z)=i \csc(iz),$$ where $\mathrm{csch}$ denotes the hyperbolic cosecant and $\csc$ denotes the cosecant.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.10$
