Difference between revisions of "Coth of a sum"
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==Theorem== | ==Theorem== | ||
The following formula holds: | The following formula holds: | ||
| − | $$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\ | + | $$\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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.27$
