Artículo
Jacobi-Sobolev-type orthogonal polynomials: second-order differential equation and zeros
Autor/es | Arvesú Carballo, Jorge
Álvarez Nodarse, Renato Marcellán Español, Francisco Pan, Ke-Lin |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 1998-04-17 |
Fecha de depósito | 2016-09-22 |
Publicado en |
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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 − ... 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. |
Agencias financiadoras | Dirección General de Enseñanza Superior. España |
Identificador del proyecto | PB 96-0120-C03-01 |
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. |
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