Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials
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Data
2010-03-01
Autores
Dimitrov, Dimitar Kolev [UNESP]
Mello, Mirela V. [UNESP]
Rafaeli, Fernando R.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Resumo
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.
Descrição
Palavras-chave
Jacobi orthogonal polynomials, Jacobi-Sobolev type orthogonal polynomials, Zeros, Monotonicity, Asymptotic
Como citar
Applied Numerical Mathematics. Amsterdam: Elsevier B.V., v. 60, n. 3, p. 263-276, 2010.