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Zbl 0744.33005
Ismail, Mourad E.H.; Li, Xin
Bound on the extreme zeros of orthogonal polynomials. (English)
[J] Proc. Am. Math. Soc. 115, No.1, 131-140 (1992). ISSN 0002-9939; ISSN 1088-6826/e

Summary: Using chain sequences we formulate a procedure to find upper (lower) bounds for the largest (smallest) zero of orthogonal polynomials in terms of their recurrence coefficients. We also apply our method to derive bounds for extreme zeros of the Laguerre, associated Laguerre, Meixner, and Meixner-Pollaczek polynomials. In addition, we consider bounds for the extreme zeros of Jacobi polynomials of degree $n$ and parameters $a\sb n$ and $b\sb n$.

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

Keywords: Meixner polynomials; Meixner-Pollaczek polynomials; Laguerre polynomials; Jacobi polynomials; extreme zeros

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