Freud's conjecture for exponential weights
Authors:
D. S. Lubinsky, H. N. Mhaskar and E. B. Saff
Journal:
Bull. Amer. Math. Soc. 15 (1986), 217221
MSC (1985):
Primary 42C05; Secondary 33A65, 41A10
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
(83j:81067), http://dx.doi.org/10.1016/01968858(80)900081
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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
(54 #7913)
 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
(87i:41024), http://dx.doi.org/10.1016/00219045(86)900675
 5.
D.
S. Lubinsky, Even entire functions absolutely monotone in
[0,∞) and weights on the whole real line, Orthogonal polynomials
and applications (BarleDuc, 1984) Lecture Notes in Math.,
vol. 1171, Springer, Berlin, 1985, pp. 221–229. MR 838987
(88d:41040), http://dx.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., SpringerVerlag, 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
(87h:42039), http://dx.doi.org/10.1016/00219045(86)900882
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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
(85j:42045), http://dx.doi.org/10.1007/BF01890022
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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
(86b:42024), http://dx.doi.org/10.1090/S00029947198507687227
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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
(86b:41024), http://dx.doi.org/10.1090/S00029947198407488380
 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
(86b:41015), http://dx.doi.org/10.1090/S027309791984153035
 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
(86a:41004), http://dx.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 SolidState Sciences, vol. 58, SpringerVerlag,
Berlin, 1985. MR
798478 (86g:81004)
 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
(86b:41029)
 1.
 D. Bessis, C. Itzykson, and J. B. Zuber, Quantum field theory techniques in graphical enumeration, Adv. in Appl. Math. 1 (1980), 109157. MR 603127
 2.
 G. Freud, On the coefficients in the recursion formulae of orthogonal polynomials, Proc. Royal Irish Acad. Sect. A 76 (1976), 16. 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., SpringerVerlag, 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., SpringerVerlag, Berlin and New York, 1986.
 9.
 Al. Magnus, On Freud's equations for exponential weights, J. Approximation Theory 46 (1986), 6599. 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), 6369. 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), 495505. MR 768722
 12.
 H. N. Mhaskar and E. B. Saff, Extremal problems for polynomials with exponential weights, Trans. Amer. Math. Soc. 285 (1984), 203234. 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), 351354. 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), 7191. 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, SpringerVerlag, 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. 219256. MR 754347
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Additional Information
DOI:
http://dx.doi.org/10.1090/S027309791986154807
PII:
S 02730979(1986)154807
