Limits of zeroes of recursively defined polynomials
- 1 November 1975
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 72 (11) , 4209
- https://doi.org/10.1073/pnas.72.11.4209
Abstract
Let {P(n)(z)} be a sequence of polynomials satisfying a linear homogeneous recursion whose coefficients are polynomials in z. Necessary and sufficient conditions are found, subject to mild nondegeneracy conditions, that a number x be a limit of zeroes of {P(n)} in the sense that there is a sequence {z(n)} with P(n)(z(n)) = 0, z(n)-->x. An application is given to a family of polynomials arising in a map-coloring problem.Keywords
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