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Uspekhi Mat. Nauk, 2002, Volume 57, Issue 1(343), Pages 45–142 (Mi umn475)  

This article is cited in 59 scientific papers (total in 59 papers)

Padé approximants and efficient analytic continuation of a power series

S. P. Suetin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This survey reflects the current state of the theory of Padé approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory, in which one must make deductions about analytic continuation of a given power series on the basis of the known asymptotic behaviour of the poles of some sequence of Padé approximants of this series. Row and diagonal sequences are studied from this point of view. Gonchar's and Rakhmanov's fundamental results of inverse nature are presented along with results of the author.


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English version:
Russian Mathematical Surveys, 2002, 57:1, 43–141

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Document Type: Article
UDC: 517.53
MSC: Primary 41A21, 30B40, 41A20; Secondary 30E25, 30F30, 30B70, 34M50, 14K20
Received: 15.10.2001

Citation: S. P. Suetin, “Padé approximants and efficient analytic continuation of a power series”, Uspekhi Mat. Nauk, 57:1(343) (2002), 45–142; Russian Math. Surveys, 57:1 (2002), 43–141

Citation in format AMSBIB
\by S.~P.~Suetin
\paper Pad\'e approximants and efficient analytic continuation of a~power series
\jour Uspekhi Mat. Nauk
\yr 2002
\vol 57
\issue 1(343)
\pages 45--142
\jour Russian Math. Surveys
\yr 2002
\vol 57
\issue 1
\pages 43--141

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    2. S. P. Suetin, “Approximation properties of the poles of diagonal Padé approximants for certain generalizations of Markov functions”, Sb. Math., 193:12 (2002), 1837–1866  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. I. Buslaev, S. F. Buslaeva, “On the Rogers–Ramanujan Periodic Continued Fraction”, Math. Notes, 74:6 (2003), 783–793  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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