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Jacobi-Sobolev-type orthogonal polynomials: second-order differential equation and zeros

Opened Access Jacobi-Sobolev-type orthogonal polynomials: second-order differential equation and zeros

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Autor: Arvesú Carballo, Jorge
Álvarez Nodarse, Renato
Marcellán Español, Francisco
Pan, Ke-Lin
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 1998-04-17
Publicado en: Journal of Computational and Applied Mathematics, 90 (2), 135-156.
Tipo de documento: Artículo
Resumen: We obtain an explicit expression for the Sobolev-type orthogonal polynomials {Qn} associated with the inner product 〈p,q〉=∫−11 p(x)q(x)p(x)dx + A1p(1)q(1) + B1p(−1)q(−1) + A2p′(1)q′(1) + B2p′(−1)q′(−1), where p(x) = (1 − x)α(1 + x)β is the Jacobi weight function, α,β> − 1, A1,B1,A2,B2⩾0 and p, q ∈ P, the linear space of polynomials with real coefficients. The hypergeometric representation (6F5) and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in [−1, 1] is studied. Furthermore, we obtain some estimates for the largest zero of Qn(x). Such a zero is located outside the interval [−1, 1]. We deduce his dependence of the masses. Finally, the WKB analysis for the distribution of zeros is presented.
Cita: Arvesú Carballo, J., Álvarez Nodarse, R., Marcellán Español, F. y Pan, K. (1998). Jacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros. Journal of Computational and Applied Mathematics, 90 (2), 135-156.
Tamaño: 293.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/45238

DOI: 10.1016/S0377-0427(98)00005-3

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