11B37 — 3 articles found.

Zeros of a real linear recurrence of degree $n\geq 4$

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (2), 2005 pp. 41–47
Vol.27 (2) 2005
Thomas R. Hagedorn Details
(Received: 2005-01-18 )
(Received: 2005-01-18 )

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

PDF(click to download): Zeros of a real linear recurrence of degree $ngeq 4$

Values of Nörlund Euler Polynomials and Nörlund Bernoulli Polynomials

C. R. Math. Rep. Acad. Sci. Canada Vol. 26 (4) 2004, pp. 97–101
Vol.26 (4) 2004
Feng-Zhen Zhao / Tianming Wang Details
(Received: 2003-10-27 )
(Received: 2003-10-27 )

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

PDF(click to download): Values of Nörlund Euler Polynomials and Nörlund Bernoulli Polynomials

On the vanishing of cubic recurrences

C. R. Math. Rep. Acad. Sci. Canada Vol. 24 (2) 2002, pp. 72–76
Vol.24 (2) 2002
M. Kulkarni / B. Sury Details
(Received: 2001-06-10 )
(Received: 2001-06-10 )

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

PDF(click to download): On the vanishing of cubic recurrences