Rocky Mountain Journal of Mathematics

Normality concerning exceptional functions

Chunnuan Cheng and Yan Xu

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Abstract

Let $\varphi(z)(\not\equiv0)$ be a function holomorphic in a domain $D$, $k\in\mathbb{N}$, and let $\mathcal{F}$ be a family of meromorphic functions defined in $D$, all of whose zeros have multiplicity at least $k+2$ such that, for every $f\in\mathcal{F}$, $f^{(k)}(z)\neq\varphi(z)$. The non-normal sequences in $\mathcal{F}$ are characterized.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 1 (2015), 157-168.

Dates
First available in Project Euclid: 7 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1428412776

Digital Object Identifier
doi:10.1216/RMJ-2015-45-1-157

Mathematical Reviews number (MathSciNet)
MR3334207

Zentralblatt MATH identifier
1311.30010

Keywords
Meromorphic functions normal family exception function

Citation

Cheng, Chunnuan; Xu, Yan. Normality concerning exceptional functions. Rocky Mountain J. Math. 45 (2015), no. 1, 157--168. doi:10.1216/RMJ-2015-45-1-157. https://projecteuclid.org/euclid.rmjm/1428412776


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