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Mat. Sb., 1992, Volume 183, Number 5, Pages 43–62 (Mi msb1122)  

This article is cited in 21 scientific papers (total in 22 papers)

Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality

A. I. Aptekarev

Abstract: The well-known Mehler–Heine asymptotic formula for the classical Jacobi polynomials is extended to broader classes of orthogonal polynomials.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1993, 76:1, 35–50

Bibliographic databases:

UDC: 517.5
MSC: Primary 33C45, 41A60; Secondary 42C05
Received: 15.05.1991

Citation: A. I. Aptekarev, “Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality”, Mat. Sb., 183:5 (1992), 43–62; Russian Acad. Sci. Sb. Math., 76:1 (1993), 35–50

Citation in format AMSBIB
\by A.~I.~Aptekarev
\paper Asymptotics of orthogonal polynomials in a~neighborhood of the~endpoints of the~interval of orthogonality
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 5
\pages 43--62
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 76
\issue 1
\pages 35--50

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    This publication is cited in the following articles:
    1. A. I. Aptekarev, V. S. Buyarov, I. S. Degeza, “Asymptotic behavior of the $L^p$-norms and the entropy for general orthogonal polynomials”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 373–395  mathnet  crossref  mathscinet  zmath  isi
    2. A. I. Aptekarev, A. Draux, V. A. Kalyagin, “On the asymptotics of sharp constants in Markov–Bernstein inequalities in integral metrics with classical weight”, Russian Math. Surveys, 55:1 (2000), 163–165  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Lubinsky D., “Asymptotics of Orthogonal Polynomials: Some Old, Some New, Some Identities”, Acta Appl. Math., 61:1-3 (2000), 207–256  crossref  mathscinet  zmath  isi
    4. D. N. Tulyakov, “Local asymptotics of the ratio of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure”, Sb. Math., 192:2 (2001), 299–321  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Takata T., “Asymptotic Formulae of Mehler-Heine-Type for Certain Classical Polyorthogonal Polynomials”, J. Approx. Theory, 135:2 (2005), 160–175  crossref  mathscinet  zmath  isi
    7. K. T.-R. McLaughlin, A. H. Vartanian, X. Zhou, “Asymptotics of Laurent polynomials of even degree orthogonal with respect to varying exponential weights”, Internat Math Res Papers, 2006 (2006), 1  crossref  mathscinet
    8. McLaughlin, KTR, “Asymptotics of Laurent polynomials of even degree orthogonal with respect to varying exponential weights”, International Mathematics Research Papers, 2006, 62815  mathscinet  zmath  isi  elib
    9. D. N. Tulyakov, “Difference equations having bases with powerlike growth which are perturbed by a spectral parameter”, Sb. Math., 200:5 (2009), 753–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Draux A., Moalla B., Sadik M., “Generalized Qd Algorithm and Markov-Bernstein Inequalities for Jacobi Weight”, Numer. Algorithms, 51:4 (2009), 429–447  crossref  mathscinet  zmath  adsnasa  isi
    11. Takata T., “Certain Multiple Orthogonal Polynomials and a Discretization of the Bessel Equation”, J. Math. Kyoto Univ., 49:4 (2009), 747–769  crossref  mathscinet  zmath  isi  elib
    12. D. N. Tulyakov, “Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients”, Sb. Math., 201:9 (2010), 1355–1402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Fejzullahu B.X., “Pointwise Asymptotics of the Ratio of Jacobi-Type Polynomials”, Integral Transform. Spec. Funct., 25:2 (2014), 97–110  crossref  mathscinet  zmath  isi
    14. Fejzullahu B.X., “Mehler-Heine Formulas For Orthogonal Polynomials With Respect To the Modified Jacobi Weight”, Proc. Amer. Math. Soc., 142:6 (2014), 2035–2045  crossref  mathscinet  zmath  isi
    15. V. M. Buchstaber, V. N. Dubinin, V. A. Kaliaguine, B. S. Kashin, V. N. Sorokin, S. P. Suetin, D. N. Tulyakov, B. N. Chetverushkin, E. M. Chirka, A. A. Shkalikov, “Alexander Ivanovich Aptekarev (on his 60th birthday)”, Russian Math. Surveys, 70:5 (2015), 965–973  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. Dominici D., “Mehler-Heine Type Formulas For Charlier and Meixner Polynomials”, Ramanujan J., 39:2 (2016), 271–289  crossref  mathscinet  zmath  isi
    17. Draux A., “-Coherent pairs of linear functionals and Markov-Bernstein inequalities”, J. Differ. Equ. Appl., 22:11 (2016), 1583–1608  crossref  mathscinet  zmath  isi  scopus
    18. A. I. Aptekarev, D. N. Tulyakov, “Koordinaty Khesse dlya odnoi algebraicheskoi krivoi tretego poryadka”, Preprinty IPM im. M. V. Keldysha, 2017, 054, 16 pp.  mathnet  crossref
    19. A. I. Aptekarev, A. Draux, D. N. Tulyakov, “On asymptotics of the sharp constants of the Markov–Bernshtein inequalities for the Sobolev spaces with coherent weights”, Preprinty IPM im. M. V. Keldysha, 2017, 059, 20 pp.  mathnet  crossref
    20. V. A. Kostin, M. N. Nebol'sina, “To the theory of the $C_0$-operator orthogonal polynomials”, J. Math. Sci. (N. Y.), 234:3 (2018), 350–356  mathnet  crossref
    21. Aptekarev A.I., Draux A., Tulyakov D.N., “On Asymptotics of the Sharp Constants of the Markov-Bernshtein Inequalities For the Sobolev Spaces”, Lobachevskii J. Math., 39:5 (2018), 609–622  mathnet  crossref  mathscinet  zmath  isi
    22. A. I. Aptekarev, D. N. Tulyakov, “Asimptoticheskii bazis reshenii $q$-rekurrentnykh sootnoshenii vne zony blizkikh sobstvennykh znachenii”, Preprinty IPM im. M. V. Keldysha, 2018, 159, 24 pp.  mathnet  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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