Difference between revisions of "Relationship between csch and csc"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "==Theorem== The following formula holds: $$\mathrm{csch}(z)=i \csc(iz),$$ where $\csch$ denotes the hyperbolic cosecant and $\csc$ denotes the cosecant. ==Proof=...")
 
 
(2 intermediate revisions by the same user not shown)
Line 2: Line 2:
 
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=}}: 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