Orthogonal polynomials defined by a recurrence relation

Author:
Paul G. Nevai

Journal:
Trans. Amer. Math. Soc. **250** (1979), 369-384

MSC:
Primary 42C05

MathSciNet review:
530062

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Abstract: R. Askey has conjectured that if a system of orthogonal polynomials is defined by the three term recurrence relation

**[1]**K. M. Case,*Orthogonal polynomials revisited*, Theory and application of special functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975) Academic Press, New York, 1975, pp. 289–304. Math. Res. Center, Univ. Wisconsin, Publ. No. 35. MR**0390322****[2]**J. Favard,*Sur les polynomes de Tchebicheff*, C. R. Acad. Sci. Paris**200**(1935), 2052-2053.**[3]**Paul G. Nevai,*Orthogonal polynomials*, Mem. Amer. Math. Soc.**18**(1979), no. 213, v+185. MR**519926**, 10.1090/memo/0213**[4]**-,*On orthogonal polynomials*, J. Approximation Theory (to appear).**[5]**Paul G. Nevai,*Distribution of zeros of orthogonal polynomials*, Trans. Amer. Math. Soc.**249**(1979), no. 2, 341–361. MR**525677**, 10.1090/S0002-9947-1979-0525677-5**[6]**G. Szegö,*Orthogonal polynomials*, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1967.

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0530062-6

Article copyright:
© Copyright 1979
American Mathematical Society