Let $f$ be oeprator monotone for some open interval $I$ of $\mathbb{R}$.
It is known that $f$ has the analytic continuation on $\mathbb{H}_+\cup I \cup \mathbb{H}_-$,
where $\mathbb{H}_+$ (resp. $\mathbb{H}_-$) is the upper (resp. the lower) half plane
of $\mathbb{C}$.
In this note, we determine the form of rational operator monotone functions by
using elementary argument, and prove the operator monotonicity of some
meromorphic functions.
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