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A Proof of Freud Conjecture About the Orthogonal Polynomials Related To [x]rho-exp[-x2m], for Integer-m

Bibliographic reference Magnus, AP.. A Proof of Freud Conjecture About the Orthogonal Polynomials Related To [x]rho-exp[-x2m], for Integer-m. In: Lecture Notes in Mathematics, Vol. 1171, p. 362-372 (1985)
Permanent URL http://hdl.handle.net/2078.1/54602
  1. Bessis D., A new method in the combinatorics of the topological expansion, 10.1007/bf01221445
  2. T.S. CHIHARA An Introduction to Orthogonal Polynomials. Gordon & Breach, NY, 1978.
  3. B. DANLOY Construction of gaussian quadrature formulas for ε∞ 0 e−x 2 f(x)dx. NFWO-FNRS Meeting Leuven 20 Nov. 1975 (unpublished). Numerical construction of orthonormal polynomials associated with an exponential weight function on a finite interval. To appear in J. Comp. Appl. Math.
  4. G. FREUD On the greatest zero of an orthogonal polynomial I Acta Sci. math. Szeged. 34(1973)91–97. II 36(1974)45–54.
  5. G. FREUD On the coefficients in the recursion formulae of orthogonal polynomials. Proc. Royal Irish Acad. 76A(1976)1–6.
  6. J.P. GASPARD Personal communication.
  7. W. HAHN Über Orthogonalpolynome und Polynomketten mit Differentialgleichung. Bericht Nr. 29(1975) Matn.-Stat. Sektion Graz. Orthogonal polynomials satisfying linear functional equations, these Proceedings.
  8. E. HENDRIKSEN, H. van ROSSUM A Padé-type approach to non-classical orthogonal polynomials. J. Math. An. Appl. Semi-classical orthogonal polynomials, these Proceedings.
  9. E. LAGUERRE Sur la réduction en fractions continues d'une fraction qui satisfait à une équation différentielle linéaire du premier ordre dont les coefficients sont rationnels. J. de Math. 1(1885)135–165=Oeuvres II 685–711, Chelsea 1972.
  10. Lew John S, Quarles Donald A, Nonnegative solutions of a nonlinear recurrence, 10.1016/0021-9045(83)90154-5
  11. D.S. LUBINSKY Estimates of Freud-Christoffel functions for some weights with the whole real line as support. J. Approx. Th.
  12. Lubinsky D. S., A weighted polynomial inequality, 10.1090/s0002-9939-1984-0754716-9
  13. D.S. LUBINSKY On Nevai's bounds for orthogonal polynomials associated with exponential weights. Submitted to J. Approx. Th.
  14. Lubinsky D. S., Sharif A., On the largest zeroes of orthogonal polynomials for certain weights, 10.1090/s0025-5718-1983-0701634-5
  15. Magnus Alphonse, Riccati acceleration of Jacobi continued fractions and Laguerre-Hahn orthogonal polynomials, Lecture Notes in Mathematics (1984) ISBN:9783540133643 p.213-230, 10.1007/bfb0099620
  16. A.P. MAGNUS On Freud's equations for exponential weights. Submitted to J. Approx. Th.
  17. A. MÁTÉ, P. NEVAI, T. ZASLAVSKY Asymptotic expansions of ratios of coefficients of orthogonal polynomials with exponential weights. Trans. AMS
  18. Mhaskar H. N., Saff E. B., Extremal problems for polynomials with exponential weights, 10.1090/s0002-9947-1984-0748838-0
  19. Mhaskar H. N., Saff E. B., Where does the sup norm of a weighted polynomial live? : A generalization of incomplete polynomials, 10.1007/bf01890023
  20. Неваи Г. П., Многочлены, ортонормальнье на вещественной оси с весом 335-1335-1335-1. Ы, 10.1007/bf01958044
  21. P. NEVAI Orthogonal polynomials associated with exp(−x4). Canad. Math. Soc. Conf. Proc. 3(1983)263–285. Asymptotics for orthogonal polynomials associated with exp(−x4). SIAM J. Math. An. 15(1984)1177–1187.
  22. P. NEVAI Two of my favorite ways of obtaining asymptotics for orthogonal polynomials, in R.L. STENS P.L. BUTZER, B. SZ.-NAGY, editors: Functional Analysis and Approximation, ISNM65 Birkhauser, Basel 1984 pp 417–436.
  23. P. NEVAI Exact bounds for orthogonal polynomials associated with exponential weights. J. Approx. Th.
  24. Nevai Paul G., Dehesa Jesus S., On Asymptotic Average Properties of Zeros of Orthogonal Polynomials, 10.1137/0510107
  25. Rakhmanov E A, ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE REAL AXIS, 10.1070/sm1984v047n01abeh002636
  26. Rossum H. van, Systems of orthogonal and quasi orthogonal polynomials connected with the padé table. III, 10.1016/s1385-7258(55)50092-8
  27. R. SHEEN Orthogonal polynomials associated with exp(-x6/6). Ph. D.Ohio State. 1984
  28. Shohat J., A differential equation for orthogonal polynomials, 10.1215/s0012-7094-39-00534-x
  29. Ullman J. L., Orthogonal polynomials associated with an infinite interval., 10.1307/mmj/1029002408
  30. O'Reilly E P, Weaire D, On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians, 10.1088/0305-4470/17/12/011
  31. P. NEVAI Orthogonal polynomials on infinite intervals. Rend. Sem. Mat. Univ. Politec. Torino.