Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials

Author(s)

Dimitrov, Dimitar K. ^[1] ; Mello, Mirela V. ^[1] ; Rafaeli, Fernando R. ^[2]

Affiliation

^[1] Univ Estadual Paulista, IBILCE, Dept Ciencias Computacao & Estatist, Sao Paulo - Brazil

^[2] Univ Estadual Campinas, Inst Matemat Estatist & Computacao Cient, BR-13081970 Campinas, SP - Brazil

• Document type: Journal article
• Source: APPLIED NUMERICAL MATHEMATICS; v. 60, n. 3, p. 263-276, MAR 2010.
• Web of Science Citations: 15

Abstract

Consider the inner product < p, q > = Gamma(alpha + beta + 2)/2(alpha+beta+1) Gamma (alpha + 1)Gamma(beta +1) integral(t)(-t) p(x)q(x)(alpha) (1 + x)(beta) dx + Mp(1)q(1)+ Np'(1)q'(1) + 1 (M) over tildep(-1)q(-1)+ (N) over tildep'(-1)q'(-1) where alpha, beta > -1 and M,N,(M) over tilde,(N) over tilde >= 0. If mu = (M,N,(M) over tilde,(N) over tilde), we denote by x(n,k)(mu)(alpha,beta), k =1,...n, the zeros of the n-th polynomial P(n)((alpha,beta,mu)) (x), orthogonal with respect to the above inner product. We investigate the location, interlacing properties, asymptotics and monotonicity of x(n,k)(mu)(alpha,beta) with respect to the parameters M, N,(M) over tilde,(N) over tilde in two important cases, when either i = N = 0 or N = 0. The results are obtained through careful analysis of the behavior and the asymptotics of the zeros of polynomials of the form p,,(x)= hn(x) + cgn(x) as functions of (C) 2010 IMACS. Published by Elsevier BA/. All rights reserved. (AU)

• FAPESP's process: 03/01874-2 - Orthogonal and similar polynomials: properties and applications
• Grantee: Alagacone Sri Ranga
• Support Opportunities: Research Projects - Thematic Grants