Derivatives of meromorphic functions of finite order

Kohs, Werner P.; Williamson, Jack

doi:10.1090/S0002-9947-1988-0933316-X

Derivatives of meromorphic functions of finite order
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by Werner P. Kohs and Jack Williamson PDF

Trans. Amer. Math. Soc. 306 (1988), 765-772 Request permission

Abstract:

Let $F$ be a nonentire, meromorphic function of finite order with only real zeros and real poles such that $F’$ has no zeros. We classify all such real $F$ and all such strictly nonreal $F$ whose poles are of bounded multiplicities. We also give examples of such $F$ which are strictly nonreal and whose poles are of unbounded multiplicities.

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