Polynomial Sequences with Only Real Zeros
نویسندگان
چکیده
In this paper we develop methods to provide unified approaches to the reality of zeros of polynomial sequences satisfying certain recurrence relations and then apply them to derive some known results and solve certain open problems and conjectures.
منابع مشابه
Ju l 2 00 6 A unified approach to polynomial sequences with only real zeros ∗
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...
متن کامل2 7 N ov 2 00 6 A unified approach to polynomial sequences with only real zeros ∗
We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...
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We give new sufficient conditions for a sequence of polynomials to have only real zeros based on the method of interlacing zeros. As applications we derive several well-known facts, including the reality of zeros of orthogonal polynomials, matching polynomials, Narayana polynomials and Eulerian polynomials. We also settle certain conjectures of Stahl on genus polynomials by proving them for cer...
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تاریخ انتشار 2005