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Mathematics of the USSR-Sbornik, 1988, Volume 60, Issue 2, Pages 385–394
DOI: https://doi.org/10.1070/SM1988v060n02ABEH003176
(Mi sm1873)
 

This article is cited in 1 scientific paper (total in 1 paper)

Convergence of simultaneous Padé approximants for a class of functions

V. N. Sorokin
References:
Abstract: This paper investigates rational approximations of a Markov function that have the highest order of contact with it at infinity, and whose denominators are invariant under multiplication of their argument by a root of unity of some fixed degree (such approximations are used in many number-theoretical problems). The approximations converge under mild restrictions on the measure. Moreover, the denominators of the approximants and the corresponding functions of the second kind have logarithmic asymptotics expressible in terms of a certain extremal measure which, in the simplest case, is the Tchebycheff measure. An explicit form is found for the extremal measure in the general case; in fact, the inverse of the distribution function is expressed in terms of elementary functions, the power moments are calculated, and the Markov function of the extremal measure is connected with algebraic equations and generalized hypergeometric functions.
Bibliography: 10 titles.
Received: 06.11.1985
Bibliographic databases:
UDC: 517.53
MSC: 30E10, 42C05
Language: English
Original paper language: Russian
Citation: V. N. Sorokin, “Convergence of simultaneous Padé approximants for a class of functions”, Math. USSR-Sb., 60:2 (1988), 385–394
Citation in format AMSBIB
\Bibitem{Sor87}
\by V.~N.~Sorokin
\paper Convergence of~simultaneous Pad\'e approximants for a~class of functions
\jour Math. USSR-Sb.
\yr 1988
\vol 60
\issue 2
\pages 385--394
\mathnet{http://mi.mathnet.ru//eng/sm1873}
\crossref{https://doi.org/10.1070/SM1988v060n02ABEH003176}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=889600}
\zmath{https://zbmath.org/?q=an:0633.41013|0626.30034}
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  • https://doi.org/10.1070/SM1988v060n02ABEH003176
  • https://www.mathnet.ru/eng/sm/v174/i3/p391
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
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