Abstract
Asymptotic expansions are given for orthogonal polynomials when the coefficients in the three-term recursion formula generating the orthogonal polynomials form sequences of bounded variation.
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R. Askey, M. Ismail (1984):Recurrence relations, continued fractions and orthogonal polynomials. Memoirs Amer. Math. Soc.,300:1–108.
E. Bank, M. Ismail (1985):The attractive Coulomb potential polynomials. Constr. Approx.1:103–119.
T. S. Chihara (1978): An Introduction to Orthogonal Polynomials. New York: Gordon & Breach.
J. M. Dombrowski (manuscript): Tridiagonal matrices and absolute continuity.
J. M. Dombrowski, P. Nevai (in press):Orthogonal polynomials, measures and recurrence relations. SIAM J. Math. Anal.
G. Freud (1971): Orthogonal Polynomials. New York: Pergamon Press. 1971.
J. S. Geronimo, K. M. Case (1980):Scattering theory and polynomials orthogonal on the real line. Trans. Amer. Math. Soc.,258:467–494.
A. Máté, P. Nevai (1983):Orthogonal polynomials and absolutely continuous measures. In: Approximation Theory IV (C. K. Chui, L. L. Schumaker, J. D. Ward, eds.). New York: Academic Press, pp. 611–617.
P. Nevai (1979):Orthogonal polynomials. Memoirs Amer. Math. Soc.,213:1–185.
P. Nevai (1979):Orthogonal polynomials defined by a recurrence relation. Trans. Amer. Math. Soc.,250:369–384.
H. Poincaré (1885):On linear ordinary differential and finite difference equations. Amer. J. Math.,7:203–258 (in French).
F. Pollaczek (1950):On a four parameter family of orthogonal polynomials. C. R. Acad. Sci. Paris,230:2254–2256 (in French).
F. Pollaczek (1956): On a Generalization of Jacobi Polynomials. Paris: (Mémorial des Sciences Mathématiques, vol. 121) (in French).
W. Rudin (1966): Real and Complex Analysis. New York: McGraw-Hill.
J. A. Shohat, J. D. Tamarkin (1963): The Problem of Moments. Providence, Rhode Island: American Mathematical Society (Mathematical Surveys, number 1).
G. Szegö (1975): Orthogonal Polynomials. Providence, Rhode Island: American Mathematical Society.
H. A. Yamani, W. P. Reinhardt (1975):L 2 discretization of the continuum: radical kinetic energy and Coulomb Hamiltonian. Phys. Rev. A,11:1144–1155.
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Communicated by Edward B. Saff.
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Máté, A., Nevai, P. & Totik, V. Asymptotics for orthogonal polynomials defined by a recurrence relation. Constr. Approx 1, 231–248 (1985). https://doi.org/10.1007/BF01890033
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DOI: https://doi.org/10.1007/BF01890033