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Mat. Sb., 1994, Volume 185, Number 10, Pages 39–72 (Mi msb932)  

This article is cited in 12 scientific papers (total in 12 papers)

Hermite–Padé approximants of generalized hypergeometric functions

Yu. V. Nesterenko


Abstract: Explicit constructions of functional approximants of the first and second kind are proposed for some collections of generalized hypergeometric functions. Formulas are proved that express the remainders of the approximants and the approximating polynomials themselves in terms of generalized hypergeometric functions with shifted parameters. Expansions in multidimensional continued fractions of the collections of functions considered are found. All this generalizes classical results related to the Gauss hypergeometric function.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 83:1, 189–219

Bibliographic databases:

UDC: 517.5
MSC: 30E10, 41A21, 33C20
Received: 14.10.1993

Citation: Yu. V. Nesterenko, “Hermite–Padé approximants of generalized hypergeometric functions”, Mat. Sb., 185:10 (1994), 39–72; Russian Acad. Sci. Sb. Math., 83:1 (1995), 189–219

Citation in format AMSBIB
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\by Yu.~V.~Nesterenko
\paper Hermite--Pad\'e approximants of generalized hypergeometric functions
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 10
\pages 39--72
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1309182}
\zmath{https://zbmath.org/?q=an:0849.11052}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 83
\issue 1
\pages 189--219
\crossref{https://doi.org/10.1070/SM1995v083n01ABEH003587}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TQ10000010}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Chirskii V., “On Linear Global Relations”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1998, no. 4, 62–64  mathscinet  isi
    2. Chirskii V., “Hermite-Pade Approximations for Certain Q-Basic Hypergeometric Series”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 2000, no. 2, 7–11  mathscinet  isi
    3. Huttner M., “Constructible Sets of Linear Differential Equations and Effective Rational Approximations of Polylogarithmic Functions”, Isr. J. Math., 153 (2006), 1–43  crossref  isi
    4. Damien Vergnaud, “Mesures d'indépendance linéaire de carrés de périodes et quasi-périodes de courbes elliptiques”, Journal of Number Theory, 129:6 (2009), 1212  crossref
    5. V. A. Gorelov, “On Algebraic Identities between Generalized Hypergeometric Functions”, Math. Notes, 88:4 (2010), 487–491  mathnet  crossref  crossref  mathscinet  isi
    6. V. G. Chirskii, “Recurrent relations for certain determinants”, J. Math. Sci., 182:4 (2012), 565–566  mathnet  crossref  mathscinet
    7. V. G. Chirskii, “On the arithmetic properties of generalized hypergeometric series with irrational parameters”, Izv. Math., 78:6 (2014), 1244–1260  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. V. Yu. Matveev, “Algebraicheskaya nezavisimost nekotorykh pochti poliadicheskikh ryadov”, Chebyshevskii sb., 16:3 (2015), 339–354  mathnet  elib
    9. V. G. Chirskii, “Arithmetic properties of Euler series”, Moscow University Mathematics Bulletin, 70:1 (2015), 41–43  mathnet  crossref  mathscinet
    10. V. Yu. Matveev, “Algebraicheskaya nezavisimost nekotorykh pochti poliadicheskikh ryadov”, Chebyshevskii sb., 17:3 (2016), 166–177  mathnet  elib
    11. V. G. Chirskii, “O preobrazovaniyakh periodicheskikh posledovatelnostei”, Chebyshevskii sb., 17:3 (2016), 191–196  mathnet  elib
    12. S. I. Kalmykov, D. B. Karp, “New identities for a sum of products of the Kummer functions”, Sib. elektron. matem. izv., 15 (2018), 267–276  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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