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Painleve equations for semiclassical recurrence coefficients: Research problems 96-2

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Magnus, AP. [UCL]
Document type Article de périodique (Journal article) – Article de recherche
Publication date 1996
Language Anglais
Journal information "Constructive Approximation : an international journal for approximations and expansions" - Vol. 12, no. 2, p. 303-306 (1996)
Peer reviewed yes
Publisher Springer Verlag (New York)
issn 0176-4276
e-issn 1432-0940
Publication status Publié
Affiliation UCL - SC/MATH - Département de mathématique
Links
  1. A. I. Aptekarev, A. Branquinho, F. Marcellán (1996):Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation. Pré-Publicaçoes Univ. Coimbra, Dep. Matemática, 96-04.
  2. S. Belmehdi, A. Ronveaux (1994):About nonlinear systems satisfied by the recurrence coefficients of semiclassical orthogonal polynomials. J. Approx. Theory76:351–368.
  3. Chudnovsky D. V., Riemann Monodromy Problem, Isomonodromy Deformation Equations and Completely Integrable Systems, Bifurcation Phenomena in Mathematical Physics and Related Topics (1980) ISBN:9789400990067 p.385-447, 10.1007/978-94-009-9004-3_20
  4. G. V. Chudnovsky:Padé approximation and the Riemann monodromy problem.Ibidem.
  5. D. V. Chudnovsky, G. V. Chudnovsky (1994):Explicit continued fractions and quantum gravity. Acta Appl. Math.,36:167–185.
  6. A. S. Fokas, A. R. Its, A. V. Kitaev (1991)Discrete Painlevé equations and their appearanc in quantum gravity. Comm. Math. Phys.,142:313–344; (1992):The isomonodromy approach to matrix models in 2D quantum gravity. Ibidem,147:395–430.
  7. E. Laguerre (1885):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. Math. Pures Appl. (4),1:135–165=pp. 685–711 in Oeuvres, vol. II. New York: Chelsea, 1972.
  8. A. P. Magnus (1995):Painlevé-type differential equations for the recurrence coefficients of semiclassical orthogonal polynomials. J. Comput. Appl. Math.,57:215–317. Preliminary preprint: ftp://unvie6.un.or.at/siam/opsf/pailevemagnus.tex
  9. A. P. Magnus (1995):Asymptotics for the simplest generalized Jacobi polynomials recurrence coefficients from Freud's equations: numerical explorations. Ann. Numer. Math.,2:311–325. Preprint in directory ftp://unvie6.un.or.at/siam/opsf/magnus/
  10. A. P. Magnus (preprint):Problem: Painlevé equations for semiclassical recurrence coefficients. ftp://unvie6.un.or.at/siam/opsf/magnus-painleve-problem.tex
  11. J. Nuttall (1984):Asymptotics of diagonal Hermite-Padé polynomials. J. Approx. Theory,42:299–386.
  12. J. A. Shohat (1939):A differential equation for orthogonal polynomials. Duke Math. J.,5:401–417.
Bibliographic reference Magnus, AP.. Painleve equations for semiclassical recurrence coefficients: Research problems 96-2. In: Constructive Approximation : an international journal for approximations and expansions, Vol. 12, no. 2, p. 303-306 (1996)
Permanent URL http://hdl.handle.net/2078.1/47093