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On normal families and a result of Drasin

  • J. K. Langley (a1)
Synopsis
Synopsis

We prove the following: suppose that a and b are complex numbers, with a non-zero, and that n is an integer not less than 5. Then, if F is a family of functions meromorphic in a plane domain Dsuch that, for each f in F, the equation

has no solutions in D, then F is normal in D.

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References
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1Drasin D.. Normal families and the Nevanlinna theory. Acta Math. 122 (1969), 231263.
2Hayman W. K.. Picard values of meromorphic functions and their derivatives. Ann. of Math. 70 (1959), 942.
3Hayman W. K.. Meromorphic Functions (Oxford: Clarendon, 1964).
4Hayman W. K.. Research Problems in Function Theory (London: Athlone Press, 1967).
5 Ku, Yung-Hsing. Sur les families normales de fonctions méromorphes. Sci. Sinica 21 (1978), 431445).
6Yang L. and Chang K.. Un nouveau critère et quelques applications. Sci.Sinica 14 (1965), 1262.
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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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