Thomas R. Hagedorn, Department of Mathematics and Statistics, The College of New Jersey, P.O. Box 7718, Ewing, NJ 08628-0718 USA; email: hagedorn@tcnj.edu

Abstract/Résumé:

Let \(S = \{a_i\}_{i=0}^\infty\) be a real linear recurrence of degree \(n\) with companion polynomial \(f_S(x)\). Let \(N_S\) be the zero-multiplicity for \(S\). Assume that the roots of \(f_S(x)\) are simple, real, and nondegenerate. When \(n=3\), Smiley and Picon showed \(N_S\leq 3\). When \(n=4\), we establish the sharp bound \(N_S\leq 5\). In general \(n\), we prove \(N_S \leq 2n-3\).

Soit \(S = \{a_i\}_{i=0}^{\infty}\) une suite définie par une relation de récurence linéaire réels de degré \(n\) avec polynôme charactéristique \(f_S (x)\). Désignons par \(N_S\) le zéro-multiplicité de \(S\). Supposons que les racines de \(f_S(x)\) soient simples, réelles, et non-dégénérées. Dans le cas \(n=3\), Smiley et Picon ont obtenu le resultat \(N_S \leq 3\). Dans le cas \(n=4\), nous démontrons la borne optimale \(N_S \leq 5\). Enfin nous démontrons que, étant donné un entier \(n\) quelconque, \(N_S \leq 2n-3\).

Keywords:

AMS Subject Classification: Recurrences 11B37

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Feng-Zhen Zhao / Tianming Wang

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Bernoulli polynomials, Euler polynomial, Nôrlund Bernoulli polynomials, Nôrlund Euler polynomial

AMS Subject Classification: Recurrences, Fibonacci and Lucas numbers and polynomials and generalizations, Bernoulli and Euler numbers and polynomials 11B37, 11B39, 11B68

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M. Kulkarni / B. Sury

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Recurrences 11B37

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