Difference between revisions of "Coth of a sum"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds: $$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\cosh(z_1)+\coth(z_2)},$$ where $\coth$ denotes hyperbolic cotangent. ==Proo...") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
==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)},$$ |
where $\coth$ denotes [[coth|hyperbolic cotangent]]. | where $\coth$ denotes [[coth|hyperbolic cotangent]]. | ||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Tanh of a sum|next=Halving identity for sinh}}: $4.5.27$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 01:48, 24 February 2018
Theorem
The following formula holds: $$\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): $4.5.27$
