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Proceedings of the American Mathematical Society

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On the growth of certain meromorphic solutions of arbitrary second order algebraic differential equations


Author: Steven Bank
Journal: Proc. Amer. Math. Soc. 25 (1970), 791-797
MSC: Primary 30.61; Secondary 34.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0262499-4
MathSciNet review: 0262499
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Abstract: In this note, we present two results concerning meromorphic functions on the whole finite plane, which are solutions of algebraic differential equations (i.e., equations of the form $ \Omega (z,y,dy/dz, \cdots ,{d^n}y/d{z^n}) = 0$, where $ \Omega $ is a polynomial in $ z,y,dy/dz, \cdots ,{d^n}y/d{z^n})$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0262499-4
Keywords: Algebraic differential equations, differential polynomials, growth of meromorphic functions, meromorphic solutions, Nevanlinna characteristic, exponent of convergence
Article copyright: © Copyright 1970 American Mathematical Society

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