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Sharp bounds for the extreme zeros of classical orthogonal polynomials. (English) Zbl 1206.33008
Using the property that the classical orthogonal polynomials satisfy a second order differential equation the authors obtain very sharp bounds for the extreme zeros of the polynomials in question. The numerical tests with Jacobi, Gegenbauer, Laguerre and Hermite polynomials show that the obtained bounds are better than the previously known bounds presented in different papers by Moak, Saff, Varga, Ismail, Li and Krasikov.
33C45Orthogonal polynomials and functions of hypergeometric type
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