On the kth derivatives of meromorphic functions and rational functions
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摘要: 设\,$f$\,是复平面\,$\mathbb C$\,内的超越亚纯函数, $R$\,是一个有理函数且\,$R \not\equiv0$, $k$\,是一个正整数. 并假设\,$f$\,的零点重级至少为\,$k+1$, 至多有限个零点例外. 则\,$f^{(k)}-R$\,有无限多个零点.Abstract: Let $f$ be a transcendental meromorphic function in $\mathbb C$, $R\not\equiv0$ be a rational function, and let $k$ be a positive integer. Suppose that all zeros of $f$ have multiplicity at least $k+1$, except possibly finite many. Then $f^{(k)}-R$ has infinitely many zeros.
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Key words:
- meromorphicfunction /
- Julia exceptional function /
- quasinormal family
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