Power Series Expansion for Real Area Hyperbolic Cotangent

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

for $\left\lvert{x}\right\rvert > 1$.

Proof
From Power Series Expansion for Real Inverse Hyperbolic Tangent:

for $\left\lvert{x}\right\rvert < 1$.

From Inverse Hyperbolic Tangent of Reciprocal equals Inverse Hyperbolic Cotangent


 * $\tanh^{-1} \left({\dfrac 1 x}\right) = \coth^{-1} x$

So:

Hence the result.