Difference between revisions of "Coth of a sum"

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==Theorem==
 
==Theorem==
 
The following formula holds:
 
The following formula holds:
$$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\cosh(z_1)+\coth(z_2)},$$
+
$$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\coth(z_1)+\coth(z_2)},$$
 
where $\coth$ denotes [[coth|hyperbolic cotangent]].
 
where $\coth$ denotes [[coth|hyperbolic cotangent]].
  

Latest revision as of 01:48, 24 February 2018

Theorem

The following formula holds: $$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\coth(z_1)+\coth(z_2)},$$ where $\coth$ denotes hyperbolic cotangent.

Proof

References