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Zbl 0820.33005
Campos, R.G.; Avila, L.A.
Some properties of orthogonal polynomials satisfying fourth order differential equations. (English)
[J] Glasg. Math. J. 37, No.1, 105-113 (1995). ISSN 0017-0895; ISSN 1469-509X/e

Starting from the fact that the Jacobi type, Laguerre type and Legendre type polynomials can be obtained as solutions of certain differential equation of the form $$a\sb 2 (x,n) f\sb n''(x) + a\sb 1(x,n) f\sb n'(x) + a\sb 0(x,n) f\sb n(x) = 0$$ where the coefficients depend not only on $x$, but also on $n$, and making use of a well-known equation concerning the zeros of the classical orthogonal polynomials [see the paper by the first author, SIAM J. Math. Anal. 18, 1664-1668 (1987; Zbl 0648.34021)], the authors derive some connections between the Jacobi, Laguerre and Legendre-type polynomials and the classical Jacobi, Laguerre and Legendre polynomials, respectively. Among other properties, certain bounds for the zeros of the Jacobi, Laguerre and Legendre-type polynomials are also obtained.
[N.Hayek (La Laguna)]

MSC 2000:: *33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: fourth order differential equations; Laguerre type polynomials; Jacobi type; polynomials; Legendre type polynomials

Citations: Zbl 0648.34021

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