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Riccati Acceleration of Jacobi Continued Fractions and Laguerre-hahn Orthogonal Polynomials

Bibliographic reference Magnus, Alphonse. Riccati Acceleration of Jacobi Continued Fractions and Laguerre-hahn Orthogonal Polynomials. In: Lecture Notes in Mathematics, Vol. 1071, p. 213-230 (1984)
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  1. N.I. AHIEZER Orthogonal polynomials on several intervals. Sov. Math. 1(1960)989–992. With Yu.Ya. TOMČUK: On the theory of orthogonal polynomials over several intervals, ibid. 2(1961)687–690.
  2. P. ASKEY, J. WIMP Associated Laguerre and Hermite polynomials. Proc. Edinburg R. Soc. A.
  3. G.A. BAKER Jr. Invariance properties in Hermite-Padé approximation. 86th Summer Meeting A.M.S., Toronto 1982.
  4. G.A. BAKER Jr., P. GRAVES-MORRIS Padé Approximants II, Encyc. of Math. 14. Addison-Wesley, Reading 1981.
  5. P. BARRUCAND, D. DICKINSON On the associate Legendre polyniomials, pp. 43–50 in D.T. HAIMO (ed.): Orthogonal Expansions and their Continuous Analogues, Southern Illinois U.P., Carbondale 1968.
  6. Belevitch Vitold, The Gauss Hypergeometric Ratio As a Positive Real Function, 10.1137/0513073
  7. Brezinski Claude, Padé-Type Approximation and General Orthogonal Polynomials, ISBN:9783034865593, 10.1007/978-3-0348-6558-6
  8. Draux André, Polynômes Orthogonaux Formels —, ISBN:9783540119845, 10.1007/bfb0066470
  9. W.G. FAIR Padé approximation to the solution of the Riccati equation. Math. Comp. 18(1964)627–634.
  10. Gammel J. L., Nuttall J., Note on generalized jacobi polynomials, Lecture Notes in Mathematics (1982) ISBN:9783540114833 p.258-270, 10.1007/bfb0093514
  11. Gautschi Walter, Minimal solutions of three-term recurrence relations and orthogonal polynomials, 10.1090/s0025-5718-1981-0606512-6
  12. Gragg William B., Truncation error bounds for g-fractions, 10.1007/bf02161885
  13. Gragg William B., Matrix interpretations and applications of the continued fraction algorithm, 10.1216/rmj-1974-4-2-213
  14. W. HAHN Über lineare Differentialgleichungen, deren Lösungen einer Rekursionsformel genügen, Math. Nachrichten 4(1951)1–11; II: ibid. 7(1952)85–104.
  15. W. HAHN On differential equations for orthogonal polynomials, Funkcialaj Ekvacioj 21(1978)1–9.
  16. Hahn Wolfgang, �ber Differentialgleichungen f�r Orthogonalpolynome, 10.1007/bf01547798
  17. R. HAYDOCK The recursive solution of the Schrödinger equation, pp. 215–294 in H. Ehrenreich, F. Seitz, D. Turnbull, eds: Solid State Physics 35, Ac. Press, N.Y. 1980.
  18. E. HENDRIKSEN, H van ROSSUM A Padé-type approach to non-classical orthogonal polynomials. J. Math. An. Appl.
  19. E.L. INCE Ordinary Differential Equations, Longmans Green, London 1927 = Dover, N.Y.
  20. Ishii Kazushige, Localization of Eigenstates and Transport Phenomena in the One-Dimensional Disordered System, 10.1143/ptps.53.77
  21. L. JACOBSEN, H. WAADELAND Modification of continued fractions. These Proceedings.
  22. W.B. JONES, W.J. THRON Continued Fractions. Analytic Theory and Applications. Encyc. of Math. 11 Addison Wesley 1980.
  23. Karlsson Johan, Sydow Björn, The convergence of Padé approximants to series of Stieltjes, 10.1007/bf02385822
  24. A.N. KHOVANSKII The Application of Continued Fractions and their Generalizations to Problems in Approximation Theory. Noordhoff, Groningen 1963.
  25. T.H. KOORNWINDER A further generalization of Krall’s Jacobi type polynomials. Preprint Math. Centr. Amsterdam ZW 171, 1982.
  26. Krall Allan M., Chebyshev Sets of Polynomials which Satisfy an Ordinary Differential Equation, 10.1137/1022087
  27. Kunz Hervé, Souillard Bernard, Sur le spectre des opérateurs aux différences finies aléatoires, 10.1007/bf01942371
  28. 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.
  29. Lambin Ph., Gaspard J. -P., Continued-fraction technique for tight-binding systems. A generalized-moments method, 10.1103/physrevb.26.4356
  30. Littlejohn Lance L., Shore Samuel D., Nonclassical orthogonal polynomials as solutions to second order differential equations , 10.4153/cmb-1982-040-2
  31. Y.L. LUKE The Special Functions and their Approximations II. Ac. Press N.Y. 1969.
  32. Al. MAGNUS Fractions continues généralisées et matrices infinies. Bull. Soc. Math. Belgique 29B(1977)145–159.
  33. Al. MAGNUS Recurrence coefficients for orthogonal polynomials on connected and non connected sets, pp. 150–171 in L. WUYTACK, ed.: Padé Approximation and its Applications, Lect.Notes Math. 765. Springer Berlin 1979.
  34. P. MARONI Sur la continuité absolue de la mesure liée à la suite des polynômes orthogonaux associés à une suite orthogonale donnée. Colloque d’Analyse Numérique. Belgadère 1982.
  35. J. MEINGUET On the solubility of the Cauchy interpolation problem, pp. 137–163 in A. TALBOT, ed.: Approximation Theory, Ac Press, London 1970.
  36. P. NEVAI Two of my favorite ways of obtaining asymptotics for orthogonal polynomials. Oberwolfach 1983.
  37. Nuttall J, Singh S.R, Orthogonal polynomials and Padé approximants associated with a system of arcs, 10.1016/0021-9045(77)90117-4
  38. Nuttall J., THE CONVERGENCE OF PADÉ APPROXIMANTS TO FUNCTIONS WITH BRANCH POINTS, Pade and Rational Approximation (1977) ISBN:9780126141504 p.101-109, 10.1016/b978-0-12-614150-4.50013-7
  39. J. NUTTALL Asymptotics of diagonal Hermite-Padé polynomials. Preprint Univ. Western Ontario 1983.
  40. O. PERRON Die Lehre von den Kettenbrüchen, 2nd ed. Teubner, Leipzig 1929 = Chelsea, N.Y.
  41. Shohat J., A differential equation for orthogonal polynomials, 10.1215/s0012-7094-39-00534-x
  42. Stokes A.N., Continued fraction solutions of the Riccati equation, 10.1017/s0004972700005219
  43. Thron W. J., Waadeland Haakon, Modifications of continued fractions, a survey, Lecture Notes in Mathematics (1982) ISBN:9783540115670 p.38-66, 10.1007/bfb0093304
  44. Turchi P, Ducastelle F, Treglia G, Band gaps and asymptotic behaviour of continued fraction coefficients, 10.1088/0022-3719/15/13/017
  45. W. WAADELAND Differential equations and modifications of continued fractions, some simple observations. Det Kong. Norske Vidensk. Selskab Skrifter 1(1983)136–150.
  46. H.S. WALL Analytic Theory of Continued Fractions. van Nostrand N.Y. 1948.
  47. Werner Helmut, Calculations of Singularities for Solutions of Algebraic Differential Equations, Computational Aspects of Complex Analysis (1983) ISBN:9789400971233 p.325-360, 10.1007/978-94-009-7121-9_14
  48. J. WIMP Computations with Recurrence Relations. Pitman, Boston, 1984.