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A Construction of Meromorphic Functions with Prescribed Asymptotic Behavior

Published online by Cambridge University Press:  22 January 2016

J.L. Stebbins
J.L. Stebbins*
Affiliation:
University of Wisconsin-Milwaukee Milwaukee, WisconsinU.S.A.
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Although there are several constructions of meromorphic functions with prescribed asymptotic sets [e.g., 5,6], it is usually difficult to determine or prescribe the nature of the asymptotic paths used in these constructions. On the other hand, there are several other constructions of meromorphic functions with prescribed asymptotic paths [e.g., 1, 10, 12], but the extent of the asymptotic values for these functions cannot always be restricted to the values approached along the given paths. Gross [3] has accomplished both results by prescribing paths for every value in the extended complex plane.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 41 , February 1971 , pp. 75 - 87
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

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