Hyperbolic Cotangent Function is Odd

Theorem
Let $\coth: \C \to \C$ be the hyperbolic cotangent function on the set of complex numbers.

Then $\coth$ is odd:


 * $\map \coth {-x} = -\coth x$

Also see

 * Hyperbolic Sine Function is Odd
 * Hyperbolic Cosine Function is Even
 * Hyperbolic Tangent Function is Odd
 * Hyperbolic Secant Function is Even
 * Hyperbolic Cosecant Function is Odd


 * Cotangent Function is Odd