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- W2029496695 abstract "We obtain an explicit expression for the Sobolev-type orthogonal polynomials { Q n } associated with the inner product 〈p,q〉= ∫ −1 1 p(x)q(x)p(x) dx + A 1 p(1)q(1) + B 1 p(−1)q(−1) + A 2 p′(1)q′(1) + B 2 p′(−1)q′(−1) , where p ( x ) = (1 − x ) α (1 + x ) β is the Jacobi weight function, α , β > − 1, A 1 , B 1 , A 2 , B 2 ⩾0 and p , q ∈ P, the linear space of polynomials with real coefficients. The hypergeometric representation ( 6 F 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 his dependence of the masses. Finally, the WKB analysis for the distribution of zeros is presented." @default.
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- W2029496695 title "Jacobi-Sobolev-type orthogonal polynomials: Second-order differential equation and zeros" @default.
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