Asymptotics of Type I Hermite–Padé Polynomials for Semiclassical Functions
Type I Hermite–Padé polynomials for a set of functions We discuss in more detail the case when From methodological considerations and in order to make the situation clearer, we start our exposition with the better known case of Padé approximants (when
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| Published in | Modern Trends in Constructive Function Theory Vol. 661; pp. 199 - 228 |
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American Mathematical Society
31.03.2016
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| Series | Contemporary Mathematics |
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| ISBN | 1470425343 9781470425340 |
| ISSN | 0271-4132 1098-3627 |
| DOI | 10.1090/conm/661/13283 |
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| Abstract | Type I Hermite–Padé polynomials for a set of functions
We discuss in more detail the case when
From methodological considerations and in order to make the situation clearer, we start our exposition with the better known
case of Padé approximants (when |
|---|---|
| AbstractList | Type I Hermite–Padé polynomials for a set of functions
We discuss in more detail the case when
From methodological considerations and in order to make the situation clearer, we start our exposition with the better known
case of Padé approximants (when |
| Author | Rakhmanov, Evguenii A. Suetin, Sergey P. Martínez-Finkelshtein, Andrei |
| Author_xml | – sequence: 1 givenname: Andrei surname: Martínez-Finkelshtein fullname: Martínez-Finkelshtein, Andrei email: andrei@ual.es organization: Department of Mathematics, University of Almería, SPAIN, and Instituto Carlos I de Física Teórica y Computacional, Granada University, SPAIN – sequence: 2 givenname: Evguenii A. surname: Rakhmanov fullname: Rakhmanov, Evguenii A. email: rakhmano@mail.usf.edu organization: Department of Mathematics, University of South Florida, USA – sequence: 3 givenname: Sergey P. surname: Suetin fullname: Suetin, Sergey P. email: suetin@mi.ras.ru organization: Steklov Mathematical Institute of Russian Academy of Sciences, Russia |
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| Keywords | WKB approximation convergence zero distribution rational approximation Padé approximation Hermite–Padé polynomials differential equations |
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| References_xml | – reference: Alexander I. Aptekarev, Arno B. J. Kuijlaars, and Walter Van Assche, Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0), Int. Math. Res. Pap. IMRP (2008), Art. ID rpm007, 128 pp. MR 2470572 (2010m:41020) – reference: J. Arvesú, J. Coussement, and W. Van Assche, Some discrete multiple orthogonal polynomials, Proceedings of the Sixth International Symposium on Orthogonal Polynomials, Special Functions and their Applications (Rome, 2001), 2003, pp. 19–45. MR 1985676 (2004g:33015), DOI 10.1016/S0377-0427(02)00597-6 – reference: F. Marcellán, A. Martínez-Finkelshtein, and P. Martínez-González, Electrostatic models for zeros of polynomials: old, new, and some open problems, J. Comput. Appl. Math. 207 (2007), no. 2, 258–272. MR 2345246 (2008h:33017), DOI 10.1016/j.cam.2006.10.020 – reference: Kouichi Takemura, On the Heun equation, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 366 (2008), no. 1867, 1179–1201. MR 2377689 (2009b:34274), DOI 10.1098/rsta.2007.2065 – reference: M. V. Fedoryuk, Asymptotics of the spectrum of the Heune equation and of Heune functions, Izv. Akad. Nauk SSSR Ser. Mat. 55 (1991), no. 3, 631–646 (Russian); English transl., Math. USSR-Izv. 38 (1992), no. 3, 621–635. MR 1129829 (93d:34003) – reference: N. S. Landkof, Foundations of modern potential theory, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy; Die Grundlehren der mathematischen Wissenschaften, Band 180. MR 0350027 (50 \#2520) – reference: D. V. Chudnovsky and G. V. Chudnovsky, The Wronskian formalism for linear differential equations and Padé approximations, Adv. in Math. 53 (1984), no. 1, 28–54. MR 748895 (86i:11038), DOI 10.1016/0001-8708(84)90016-1 – reference: A. A. Gonchar and E. A. Rakhmanov, Equilibrium distributions and the rate of rational approximation of analytic functions, Mat. Sb. 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| Snippet | Type I Hermite–Padé polynomials for a set of functions
We discuss in more detail the case when
From methodological considerations and in order to make the... |
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