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Asymptotic behavior of polynomials satisfying three-term recurrence relations

✍ Scribed by William B Jones; W.J Thron; Nancy J Wyshinski

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
1010 KB
Volume
71
Category
Article
ISSN
0021-9045

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In this paper, we give the canonical expression for an inner product (defined in \(\mathscr{P}\), the linear space of real polynomials), for which the set of orthonormal polynomials satisfies a \((2 N+1)\)-term recurrence relation. This result is a generalization of Favard's theorem about orthogonal

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✍ E.K. Ifantis; P.N. Panagopoulos πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 316 KB

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 \(