Power Series Expansion for Real Area Hyperbolic Cotangent

Theorem
The (real) area hyperbolic cotangent function has a Taylor series expansion:

for $\size x > 1$.

Proof
From Power Series Expansion for Real Inverse Hyperbolic Tangent:

for $\size x < 1$.

From Real Area Hyperbolic Tangent of Reciprocal equals Real Area Hyperbolic Cotangent:


 * $\map \artanh {\dfrac 1 x} = \arcoth x$

So:

Hence the result.

Also see

 * Power Series Expansion for Real Inverse Hyperbolic Sine
 * Power Series Expansion for Real Inverse Hyperbolic Cosine
 * Power Series Expansion for Real Inverse Hyperbolic Tangent
 * Power Series Expansion for Real Area Hyperbolic Secant
 * Power Series Expansion for Real Area Hyperbolic Cosecant