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An unsolvable Cousin problem


Author: Lee A. Rubel
Journal: Proc. Amer. Math. Soc. 104 (1988), 410-412
MSC: Primary 34A20; Secondary 30D05
DOI: https://doi.org/10.1090/S0002-9939-1988-0962806-4
MathSciNet review: 962806
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Abstract: We construct a Laurent series $ \sum\nolimits_{n = - \infty }^\infty {{A_n}{z^n}} $, convergent in an annulus $ \left\{ {\rho < \left\vert z \right\vert < 1/\rho } \right\}$ for some $ \rho < 1$, which satisfies an algebraic differential equation (ADE) there, but such that neither of the series $ \sum\nolimits_{n = 0}^\infty {{A_n}{z^n}} $ and $ \sum\nolimits_{n = - \infty }^{ - 1} {{A_n}{z^n}} $ satisfies any ADE.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0962806-4
Article copyright: © Copyright 1988 American Mathematical Society

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