Arvesú Carballo, JorgeÁlvarez Nodarse, RenatoMarcellán Español, Francisco JoséPan, K.2010-01-142010-01-141998-04-17Journal of Computational and Applied Mathematics, 1998, vol. 90, n. 2, p. 135-1560377-0427https://hdl.handle.net/10016/640522 pages, 4 figures.-- MSC1991 codes: 33C45; 33A65; 42C05.-- Dedicated to Professor Mario Rosario Occorsio on his 65th birthday.MR#: MR1624329 (99h:33029)Zbl#: Zbl 0924.33006We obtain an explicit expression for the Sobolev-type orthogonal polynomials $\{Q_n\}$ associated with the inner product $\langle p,q\rangle=\int^1_{-1}p(x)q(x)\rho(x)dx+A_1p(1)q(1)+B_1p(-1)q(-1)+A_2p'(1)q'(1)+B_2p'(-1)q'(-1)$, where $\rho(x)=(1-x)^\alpha(1+x)^\beta$ is the Jacobi weight function, $\alpha,\beta>-1$, $A_1,B_1,A_2,B_2\geq 0$ and $p,q\in\bold P$, the linear space of polynomials with real coefficients. The hypergeometric representation $({}_6F_5)$ 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 $Q_n(x)$. Such a zero is located outside the interval $[-1,1]$. We deduce its dependence on the masses. Finally, the WKB analysis for the distribution of zeros is presented.application/pdfeng© ElsevierOrthogonal polynomialsJacobi polynomialsHypergeometric functionSobolev-type orthogonal polynomialsWKB methodresearch articleMatemáticas10.1016/S0377-0427(98)00005-3open access