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Newton sum rules of polynomials defined by a three-term recurrence relation

โœ Scribed by P. Natalini; P.E. Ricci

Book ID
104352205
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
252 KB
Volume
42
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

We derive a general formula for computing the Newton sum rules of every polynomial belonging to a given polynomial set. We use the following tools: a recursive computation of the coefficients of the given polynomial in terms of the coefficients of the three-term recurrence relation, the generalized Lucas polynomials of the first kind, and last, the Newton-Girard formulas. (~) 2001 Elsevier Science Ltd. All rights reserved.

๐Ÿ“œ SIMILAR VOLUMES

On the Zeros of a Class of Polynomials D
On the Zeros of a Class of Polynomials Defined by a Three Term Recurrence Relation
โœ E.K. Ifantis; P.N. Panagopoulos ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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 \(