Abstract
The order of the distance between zeros of orthogonal and of quasiorthogonal polynomials is determined, and also the order of the Christoffel function if the weight function w(x)= q(x)e−X satisfies certain conditions. As a special case, lower and upper bounds are found for the distance between zeros of L αn (X) + AL αn−1 (X), where L αn is the n-th order Laguerre polynomial.
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G. Freud, Orthogonale Polynome, Budapest (1969).
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E. Makai, “Über die Nullstellen von Funktionen, die Lösungen Sturm-Liouvillescher Differential-gleichungen sind,” Comm. Math. Helvetici,16, 153–199 (1944).
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Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 511–520, May, 1971.
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Freud, G. A class of orthogonal polynomials. Mathematical Notes of the Academy of Sciences of the USSR 9, 295–300 (1971). https://doi.org/10.1007/BF01094355
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DOI: https://doi.org/10.1007/BF01094355