Power Series Expansion for Real Area Hyperbolic Cosine/Also presented as

Power Series Expansion for Real Area Hyperbolic Cosine: Also presented as
Some sources present this result in the form:

This takes into account the interpretation that $\cosh^{-1} x$ is a multifunction arising from the fact that $\cosh x = \map \cosh {-1}$ for $size x \ge 1$.