Freud's conjecture for exponential weights

Authors:
D. S. Lubinsky, H. N. Mhaskar and E. B. Saff

Journal:
Bull. Amer. Math. Soc. **15** (1986), 217-221

MSC (1985):
Primary 42C05; Secondary 33A65, 41A10

DOI:
https://doi.org/10.1090/S0273-0979-1986-15480-7

MathSciNet review:
854558

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References | Similar Articles | Additional Information

**1.**D. Bessis, C. Itzykson, and J. B. Zuber,*Quantum field theory techniques in graphical enumeration*, Adv. in Appl. Math.**1**(1980), no. 2, 109–157. MR**603127**, https://doi.org/10.1016/0196-8858(80)90008-1**2.**Géza Freud,*On the coefficients in the recursion formulae of orthogonal polynomials*, Proc. Roy. Irish Acad. Sect. A**76**(1976), no. 1, 1–6. MR**0419895****3.**A. Knopfmacher, D. S. Lubinsky, and P. Nevai,*Freud's conjecture and approximation of reciprocals of weights by polynomials*(manuscript).**4.**D. S. Lubinsky,*Gaussian quadrature, weights on the whole real line and even entire functions with nonnegative even order derivatives*, J. Approx. Theory**46**(1986), no. 3, 297–313. MR**840397**, https://doi.org/10.1016/0021-9045(86)90067-5**5.**D. S. Lubinsky,*Even entire functions absolutely monotone in [0,∞) and weights on the whole real line*, Orthogonal polynomials and applications (Bar-le-Duc, 1984) Lecture Notes in Math., vol. 1171, Springer, Berlin, 1985, pp. 221–229. MR**838987**, https://doi.org/10.1007/BFb0076547**6.**D. S. Lubinsky and E. B. Saff,*Uniform and mean approximation by certain weighted polynomials, with applications*(manuscript).**7.**D. S. Lubinsky, H. N. Mhaskar, and E. B. Saff,*A proof of Freud's Conjecture for exponential weights*(manuscript).**8.**Al. Magnus,*A proof of Freud's Conjecture about orthogonal polynomials related to |x|*exp (-*x*), Orthogonal Polynomials and Their Applications (C. Brezinski et al., eds.) Lecture Notes in Math., Springer-Verlag, Berlin and New York, 1986.**9.**Alphonse P. Magnus,*On Freud’s equations for exponential weights*, J. Approx. Theory**46**(1986), no. 1, 65–99. Papers dedicated to the memory of Géza Freud. MR**835728**, https://doi.org/10.1016/0021-9045(86)90088-2**10.**Attila Máté, Paul Nevai, and Vilmos Totik,*Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle*, Constr. Approx.**1**(1985), no. 1, 63–69. MR**766095**, https://doi.org/10.1007/BF01890022**11.**Attila Máté, Paul Nevai, and Thomas Zaslavsky,*Asymptotic expansions of ratios of coefficients of orthogonal polynomials with exponential weights*, Trans. Amer. Math. Soc.**287**(1985), no. 2, 495–505. MR**768722**, https://doi.org/10.1090/S0002-9947-1985-0768722-7**12.**H. N. Mhaskar and E. B. Saff,*Extremal problems for polynomials with exponential weights*, Trans. Amer. Math. Soc.**285**(1984), no. 1, 203–234. MR**748838**, https://doi.org/10.1090/S0002-9947-1984-0748838-0**13.**H. N. Mhaskar and E. B. Saff,*Weighted polynomials on finite and infinite intervals: a unified approach*, Bull. Amer. Math. Soc. (N.S.)**11**(1984), no. 2, 351–354. MR**752796**, https://doi.org/10.1090/S0273-0979-1984-15303-5**14.**H. N. Mhaskar and E. B. Saff,*Where does the sup norm of a weighted polynomial live? (A generalization of incomplete polynomials)*, Constr. Approx.**1**(1985), no. 1, 71–91. MR**766096**, https://doi.org/10.1007/BF01890023**15.**H. N. Mhaskar and E. B. Saff,*Where does the L*? (manuscript).**16.**P. Nevai, Geza Freud,*Christoffel functions and orthogonal polynomials*(*A case study*), J. Approximation Theory (to appear).**17.**D. G. Pettifor and D. L. Weaire (eds.),*The recursion method and its applications*, Springer Series in Solid-State Sciences, vol. 58, Springer-Verlag, Berlin, 1985. MR**798478****18.**E. B. Saff,*Incomplete and orthogonal polynomials*, Approximation theory, IV (College Station, Tex., 1983) Academic Press, New York, 1983, pp. 219–256. MR**754347**

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DOI:
https://doi.org/10.1090/S0273-0979-1986-15480-7