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Location of the zeros of polynomials satisfying three-term recurrence relations. III. Positive coefficients case

✍ Scribed by E Leopold

Publisher: Elsevier Science
Year: 1985
Tongue: English
Weight: 413 KB
Volume: 43
Category: Article
ISSN: 0021-9045
DOI: 10.1016/0021-9045(85)90143-1

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Let \(P\_{N+1}(x)\) be the polynomial which is defined recursively by \(P\_{0}(x)=0\), \(P\_{1}(x)=1, \quad\) and \(\alpha\_{n} P\_{n+1}(x)+\alpha\_{n-1} P\_{n-1}(x)+b\_{n} P\_{n}(x)=x d\_{n} P\_{n}(x), \quad n=1, \quad 2, \ldots, N\), where \(\alpha\_{n}, b\_{n}, d\_{n}\) are real sequences with \(