Abstract:
A new method of studying the asymptotic behaviour of orthogonal polynomials in the neighbourhood of an end-point of the support of the orthogonality measure is put forward. The asymptotics in the neighbourhood of the end-point is found in terms of the asymptotics of the values of the polynomials at the point itself and the asymptotic behaviour of the coefficients of the recurrence relations. Applications of the result obtained are considered.
Citation:
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
\Bibitem{Tul01}
\by D.~N.~Tulyakov
\paper Local asymptotics of the~ratio of orthogonal polynomials in the~neighbourhood of an~end-point of the~support of the~orthogonality measure
\jour Sb. Math.
\yr 2001
\vol 192
\issue 2
\pages 299--321
\mathnet{http://mi.mathnet.ru/eng/sm547}
\crossref{https://doi.org/10.1070/sm2001v192n02ABEH000547}
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Linking options:
https://www.mathnet.ru/eng/sm547
https://doi.org/10.1070/sm2001v192n02ABEH000547
https://www.mathnet.ru/eng/sm/v192/i2/p139
This publication is cited in the following 15 articles:
A. I. Aptekarev, “Giperbolicheskii ob'em 3-d mnogoobrazii, A-mnogochleny, chislennye proverki gipotez”, Preprinty IPM im. M. V. Keldysha, 2023, 052, 36 pp.
Alexander Ivanovich Aptekarev, “Hyperbolic volume of 3-d manifolds, A-polynomials, numerical hypothesis testing”, KIAM Prepr., 2023, no. 52-e, 1
A. I. Aptekarev, S. Yu. Dobrokhotov, D. N. Tulyakov, A. V. Tsvetkova, “Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and
recurrence relations”, Izv. Math., 86:1 (2022), 32–91
A. I. Aptekarev, T. V. Dudnikova, D. N. Tulyakov, “Volume Conjecture and WKB Asymptotics”, Lobachevskii J Math, 43:8 (2022), 2057
Aptekarev A.I. Dudnikova T.V. Tulyakov D.N., “Recurrence Relations and Asymptotics of Colored Jones Polynomials”, Lobachevskii J. Math., 42:11, SI (2021), 2580–2595
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
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.
A. I. Aptekarev, D. N. Tulyakov, “Koordinaty Khesse dlya odnoi algebraicheskoi krivoi tretego poryadka”, Preprinty IPM im. M. V. Keldysha, 2017, 054, 16 pp.
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.
Dominici D., “Mehler-Heine Type Formulas For Charlier and Meixner Polynomials”, Ramanujan J., 39:2 (2016), 271–289
B.X.h. Fejzullahu, “Pointwise asymptotics of the ratio of Jacobi-type polynomials”, Integral Transforms and Special Functions, 2013, 1
D. N. Tulyakov, “Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients”, Sb. Math., 201:9 (2010), 1355–1402
D. N. Tulyakov, “Difference equations having bases with powerlike growth which are perturbed by a spectral parameter”, Sb. Math., 200:5 (2009), 753–781
Takata T., “Asymptotic formulae of Mehler-Heine-type for certain classical polyorthogonal polynomials”, J. Approx. Theory, 135:2 (2005), 160–175
A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72
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