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

Full-text PDF Free Access

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), 109-157. MR**603127****2.**G. Freud,*On the coefficients in the recursion formulae of orthogonal polynomials*, Proc. Royal Irish Acad. Sect. A 76 (1976), 1-6. MR**419895****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. Approximation Theory (to appear). MR**840397****5.**D. S. Lubinsky,*Even entire functions absolutely monotone in*[0, ∞)*and weights on the whole real line*, Orthogonal Polynomials and Their Applications (C. Brezinski et al., eds.), Lecture Notes in Math., Springer-Verlag, Berlin and New York, 1986. MR**838987****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.**Al. Magnus,*On Freud's equations for exponential weights*, J. Approximation Theory 46 (1986), 65-99. MR**835728****10.**A. Máté, P. Nevai, and V. Totik,*Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle*, Constr. Approx. 1 (1985), 63-69. MR**766095****11.**A. Máté, P. Nevai, and T. Zaslavsky,*Asymptotic expansion of ratios of coefficients of orthonormal polynomials with exponential weights*, Trans. Amer. Math. Soc. 287 (1985), 495-505. MR**768722****12.**H. N. Mhaskar and E. B. Saff,*Extremal problems for polynomials with exponential weights*, Trans. Amer. Math. Soc. 285 (1984), 203-234. MR**748838****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), 351-354. MR**752796****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), 71-91. MR**766096****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 Physics, vol. 58, Springer-Verlag, Berlin and New York, 1984. MR**798478****18.**E. B. Saff,*Incomplete and orthogonal polynomials*, Approximation Theory IV (C. K. Chui et al., eds.), 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