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Mat. Sb., 1991, Volume 182, Number 2, Pages 283–302 (Mi msb1295)  

This article is cited in 9 scientific papers (total in 9 papers)

On arithmetic properties of the values of hypergeometric functions

P. L. Ivankov


Abstract: The author proposes an effective method of constructing a linear approximating form for a hypergeometric function of general type and its derivatives, which has a zero of the maximal possible order at $z=0$. This construction is applied to the study of arithmetic properties of values of these functions at points of an imaginary quadratic field.

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English version:
Mathematics of the USSR-Sbornik, 1992, 72:1, 267–286

Bibliographic databases:

UDC: 511.361
MSC: Primary 11J91; Secondary 11J13
Received: 18.12.1987 and 22.10.1990

Citation: P. L. Ivankov, “On arithmetic properties of the values of hypergeometric functions”, Mat. Sb., 182:2 (1991), 283–302; Math. USSR-Sb., 72:1 (1992), 267–286

Citation in format AMSBIB
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\by P.~L.~Ivankov
\paper On arithmetic properties of the values of hypergeometric functions
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 2
\pages 283--302
\mathnet{http://mi.mathnet.ru/msb1295}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1103275}
\zmath{https://zbmath.org/?q=an:0776.11039}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..72..267I}
\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 1
\pages 267--286
\crossref{https://doi.org/10.1070/SM1992v072n01ABEH001413}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JF72300014}


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  • http://mi.mathnet.ru/eng/msb/v182/i2/p283

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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. Yu. V. Nesterenko, “Hermite–Padé approximants of generalized hypergeometric functions”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 189–219  mathnet  crossref  mathscinet  zmath  isi
    2. P. L. Ivankov, “O lineinoi nezavisimosti znachenii nekotorykh funktsii”, Fundament. i prikl. matem., 1:1 (1995), 191–206  mathnet  mathscinet  zmath  elib
    3. P. L. Ivankov, “On the differentiation of a hypergeometric function with respect to the parameter”, J. Math. Sci., 182:4 (2012), 505–507  mathnet  crossref  mathscinet
    4. Merila V., “On the Linear Independence of the Values of Gauss Hypergeometric Function”, Acta Arith., 144:4 (2010), 349–371  crossref  mathscinet  zmath  isi
    5. Merila V., “A Nonvanishing Lemma for Certain Pade Approximations of the Second Kind”, Int. J. Number Theory, 7:8 (2011), 1977–1997  crossref  mathscinet  zmath  isi
    6. Ivankov P.L., “O differentsirovanii po parametru nekotorykh funktsii”, Nauka i obrazovanie: elektronnoe nauchno-tekhnicheskoe izdanie, 2012, no. 05, 10–10  elib
    7. Pavel Ivankov, “Approximation of values of an exponential function”, S&E BMSTU, 13:10 (2013)  crossref
    8. Yu. V. Nesterenko, “On Catalan's constant”, Proc. Steklov Inst. Math., 292 (2016), 153–170  mathnet  crossref  crossref  mathscinet  isi  elib
    9. P. L. Ivankov, “O priblizhenii znachenii nekotorykh gipergeometricheskikh funktsii s irratsionalnymi parametrami”, Chebyshevskii sb., 17:1 (2016), 108–116  mathnet  elib
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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