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On the hypertranscendence of meromorphic solutions of certain functional equations

Published online by Cambridge University Press:  14 November 2011

Steven B. Bank
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, U.S.A.

Synopsis

This paper deals mainly with showing that meromorphic solutions of Poincaré functional equations cannot satisfy algebraic differential equations. Results of this type for entire solutions have previously been obtained by H. Wittich.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

1Bank, S.. On determining the growth of meromorphic solutions of algebraic differential equations having arbitrary entire coefficients. Nagoya Math. J. 49 (1973), 5365.Google Scholar
2Bank, S. and Kaufman, R.. A note on Holder's theorem concerning the Gamma function. Math. Ann. 232 (1978), 115120.Google Scholar
3Bank, S. and Kaufman, R.. An extension of Holder's theorem concerning the Gamma function. Funkcial. Ekvac. 19 (1976), 5363.Google Scholar
4Bank, S. and Kaufman, R.. On differential equations and functional equations, (to appear).Google Scholar
5Hayman, W. K.. Meromorphic functions. Oxford Mathematical Monographs (Oxford: Clarendon Press, 1964).Google Scholar
6Miles, J.. Quotient representations of meromorphic functions. J. Analyse Math. 25 (1972), 371388.Google Scholar
7Nevanlinna, R.. Le théorème de Picard-Borei et la théorie des fonctions méromorphes (Paris: Gauthier-Villars, 1929).Google Scholar
8Poincaré, H.. Sur une classe nouvelle de transcendantes uniformes. J. Math. Pures Appl. 6 (1890), 313365.Google Scholar
9Saks, S. and Zygmund, A.. Analytic functions. Translated by Scott, E. J.. Monografie Matematyczne, 28 (Warszawa-Wrocław: Polskie Towarzystwo Matematyczyne, 1952).Google Scholar
10Valiron, G.. Fonctions Analytiques (Paris: Presses Universitaires de France, 1954).Google Scholar
11Wittich, H.. Bemerkung zu einer Functionalgleichung von H. Poincaré. Arch. Math. 1 (1950), 9095.Google Scholar
12Wittich, H.. Neure Untersuchungen über eindeutige analytische Functionen. Ergebn. Math. 8 (1955).Google Scholar