On the largest zeroes of orthogonal polynomials for certain weights

Authors:
D. S. Lubinsky and A. Sharif

Journal:
Math. Comp. **41** (1983), 199-202

MSC:
Primary 42C05; Secondary 33A65

DOI:
https://doi.org/10.1090/S0025-5718-1983-0701634-5

MathSciNet review:
701634

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Abstract | References | Similar Articles | Additional Information

Abstract: The asymptotic growth of the largest zero of the orthogonal polynomials for the weights is investigated.

**[1]**T. S. Chihara,*An Introduction to Orthogonal Polynomials*, Gordon and Breach, New York, 1978. MR**0481884 (58:1979)****[2]**T. S. Chihara, "A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials,"*Canad. Math. Bull.*, v. 13, 1970, pp. 529-532. MR**0280761 (43:6480)****[3]**G. Freud, "On the greatest zero of an orthogonal polynomial. I,"*Acta Sci. Math.*(*Hungar.*), v. 34, 1973, pp. 91-97. MR**0318761 (47:7307)****[4]**G. Freud, "On the greatest zero of an orthogonal polynomial. II,"*Acta Sci. Math.*(*Hungar.*), v. 36, 1974, pp, 49-54. MR**0346406 (49:11131)****[5]**P. G. Nevai & J. S. Dehesa, "On asymptotic average properties of zeroes of orthogonal polynomials,"*SIAM J. Math. Anal.*, v. 10, 1979, pp. 1184-1192. MR**547805 (80m:42031)****[6]**F. W. J. Olver,*Asymptotics and Special Functions*, Academic Press, New York, 1974. MR**0435697 (55:8655)****[7]**S. Wigert, "Sur les polynomes orthogonaux et l'approximation des fonctions continues,"*Ark. Mat. Astronom. Fysik*, v. 17, 1923.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0701634-5

Article copyright:
© Copyright 1983
American Mathematical Society