Abstract
In this paper, we study one conjecture proposed by W. Bergweiler and show that any transcendental meromorphic functions f(z) have the form exp(αz+β) if f(z)f″(z)–a(f′ (z))2≠0, where \( a \ne 1,\;\frac{{n \pm 1}} {n},\;n \in N \). Moreover, an analogous normality criterion is obtained.
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