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Which is the limit of validity for WKB expansion for black hole Quasi-normal modes? In many papers I see that the authors only report the overtone $n=1$. Is WKB expansion valid only for small $n$?

As an example I refer to this paper, but I could cite more.

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I have found the answer my self in this paper, were the author a pag 10 says:

The higher order WKB approach proved to be useful for finding lower overtones of the quasi normal specrtum and is in good agreement with accurate numerical data

So yes the WKB approach is accurate only for small n

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