Polynomials with rational generating functions and real zeros
This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a binomial-type denominator. We show that every member of a two-parameter family consisting of such generating functions gives rise to a sequence of polynomials \(\{P_{m}(z)\}_{m=0}^{...
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| Veröffentlicht in: | arXiv.org |
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| Hauptverfasser: | , |
| Format: | Paper |
| Sprache: | Englisch |
| Veröffentlicht: |
Ithaca
Cornell University Library, arXiv.org
11.01.2016
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| Schlagworte: | |
| ISSN: | 2331-8422 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a binomial-type denominator. We show that every member of a two-parameter family consisting of such generating functions gives rise to a sequence of polynomials \(\{P_{m}(z)\}_{m=0}^{\infty}\) that is eventually hyperbolic. Moreover, the real zeros of the polynomials \(P_{m}(z)\) form a dense subset of an interval \(I\subset\mathbb{R}^{+}\), whose length depends on the particular values of the parameters in the generating function. |
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| Bibliographie: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.1601.02582 |