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The impact of Stieltjes' work on continued fractions and orthogonal polynomials: additional material (1995)  (Make Corrections)  (6 citations)
Galliano Valent, Walter VAN ASSCHE



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Abstract: In the recent new edition of the collected works of T.J. Stieltjes, one of us gave an impression of the impact of Stieltjes' work a century after his death [43]. In this paper we give an update and mention some observations which were missing from [43] and some results which appeared during the last two years and which are directly related to Stieltjes' work. In particular there is a large section on special polynomials which were already considered by Stieltjes but which were rediscovered... (Update)

Context of citations to this paper:   More

...of the collected works of T.J. Stieltjes, one of us gave an impression of the impact of Stieltjes work a century after his death [43]. In this paper we give an update and mention some observations which were missing from [43] and some results which appeared during the last...

...extended Marden s result. We refer to Chapter 2. 9 of Marden s monograph [8] for more detailed information about Lam e s equation and to [18, 16] for the connection with electrostatics of zeros of orthogonal polynomials. In very recent papers Grunbaum [3] gave an electrostatic...

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Electrostatic Interpretation and Bounds for the Extreme Zeros of .. - Dimitrov   (Correct)
Lamé Differential Equations and Electrostatics - Dimitrov, Van Assche   (Correct)
Monotonicity of multi-point Padé approximants - Bultheel.. (1999)   (Correct)

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0.7:   Asymptotics for the zeros and poles of normalized.. - Varga, Carpenter (1994)   (Correct)
0.5:   Q-Hermite Polynomials and Classical Orthogonal Polynomials - Berg, Ismail (1995)   (Correct)

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3:   A strong Stieltjes moment problem (context) - Jones, Thron et al. - 1980
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BibTeX entry:   (Update)

Valent, G. and W. Van Assche, The impact of Stieltjes' work on continued fractions and orthogonal polynomials: additional material J. Comput. Appl. Math. 65 (1995), 419--447. http://citeseer.ist.psu.edu/valent95impact.html   More

@misc{ valent95impact,
  author = "G. Valent and W. Van Assche",
  title = "The impact of Stieltjes' work on continued fractions and orthogonal polynomials:
    additional material J",
  text = "Valent, G. and W. Van Assche, The impact of Stieltjes' work on continued
    fractions and orthogonal polynomials: additional material J. Comput. Appl.
    Math. 65 (1995), 419--447.",
  year = "1995",
  url = "citeseer.ist.psu.edu/valent95impact.html" }
Citations (may not include all citations):
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154   Orthogonal Polynomials (context) - Szego - 1975
143   Higher Transcendental Functions (context) - Erd'elyi, Magnus et al. - 1953
143   Higher Transcendental Functions (context) - Erd'elyi, Magnus et al. - 1953
67   Generalized Hypergeometric Series (context) - Bailey - 1972
66   The Askey scheme of hypergeometric orthogonal polynomials an.. - Koekoek, Swarttouw - 1994
52   Analytic Theory of Continued Fractions (context) - Wall - 1973
52   The Classical Moment Problem (context) - Akhiezer - 1965
42   Die Lehre von den Kettenbruchen (context) - Perron - 1977
37   Special Functions (context) - Rainville - 1971
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9   analogue of the Laguerre polynomials (context) - Moak, q- - 1981
8   Differenzengleichungen genugen (context) - Hahn, Orthogonalpolynome et al. - 1949
7   Expansions in Eigenfunctions of Self-Adjoint Operators (context) - Berezanskii - 1968
6   orthogonal polynomials and Christoffel functions (context) - Nevai, Freud - 1986
6   The impact of Stieltjes work on continued fractions and orth.. - Van Assche
4   the equilibrium problem for vector potentials (context) - Gonchar, Rakhmanov - 1985
4   Asymptotische Entwickelungen beschrankter Funktionen und das.. (context) - Nevanlinna - 1922
4   Birth and death processes and orthogonal polynomials (context) - Ismail, Letessier et al. - 1990
4   Orthogonale Polynomsysteme mit einer besonderen Gestalt der .. (context) - Meixner - 1934
4   The asymptotic expansion of Bessel functions of large order (context) - Olver - 1954
3   Spectral theory of Jacobi matrices (context) - Masson, Repka - 1991
3   A characterization and a class of distribution functions for.. (context) - Chihara - 1970
3   On Freud's equations for exponential weights (context) - Magnus - 1986  ACM
3   Lecture Notes in Mathematics (context) - Grosswald, Polynomials - 1978
2   Indeterminate moment problems and the theory of entire funct.. (context) - Berg  ACM
2   the zeros of generalized Bessel polynomials (context) - de Bruin, Saff et al. - 1981
2   beta integral on the unit circle and some biorthogonal ratio.. (context) - Al-Salam, Ismail et al. - 1994
2   Limits of some q-Laguerre polynomials (context) - Askey - 1986
2   Quadratic birth and death processes and associated continuou.. (context) - Ismail, Letessier et al. - 1989  ACM
2   the convergence of algebraic continued fractions whose coeff.. (context) - Van Vleck - 1904
2   Generalized orthogonality and continued fractions (context) - Ismail, Masson  ACM
1   Weak convergence of orthogonal polynomials (context) - Van Assche
1   Zur Stieltjesschen Kettenbruchtheorie (context) - Hellinger - 1922
1   The early history of the moment problem (context) - Kjeldsen - 1993
1   Electrostatic interpretation of zeros (context) - Hendriksen, van Rossum - 1988
1   Two families of associated Wilson polynomials (context) - Ismail, Letessier et al. - 1990
1   Electrostatics and the zeros of the classical polynomials (context) - Forrester, Rogers - 1986
1   Beitrage zur Konvergenztheorie der Stieltjesschen Kettenbruc.. (context) - Hamburger - 1919
1   Infinite Jacobi matrices and a matrix moment problem (context) - Krein, Krein - 1949
1   eme note sur le probl`eme des moments (context) - Riesz - 1923
1   van Dijk ed (context) - Stieltjes, Papers - 1993

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