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Chebyshevskii Sbornik, 2021, Volume 22, Issue 2, Pages 536–542
DOI: https://doi.org/10.22405/2226-8383-2018-22-2-536--1
(Mi cheb1053)
 

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

BRIEF MESSAGE

Values of hypergeometric F-series at polyadic Liouvillea points

E. Yu. Yudenkovaab

a Russian Presidential Academy of National Economy and Public Administration (Moscow)
b Moscow Pedagogical State University (Moscow)
Full-text PDF (636 kB) Citations (1)
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Abstract: This paper proves infinite algebraic independence of the values of hypergeometric F – series at polyadic Liouville points. Hypergeometric functions are defined for |z|<1 by the power series:
n=0(α1)n(αr)n(β1)n(βs)nn!zn.
F – series have form fn=n=0ann!zn whose coefficients an satisfy some arithmetic properties. These series converge in the field Qp of p – adic numbers and their algebraic extensions Kv. Polyadic number is a series of the form n=0ann!,anZ. Liouville number is a real number x with the property that, for every positive integer n, there exist infinitely many pairs of integers (p,q) with q>1 such that 0<|xpq|<1qn. The polyadic Liouville number α has the property that for any numbers P,D there exists an integer |A| such that for all primes pP the inequality |αA|p<AD.
Keywords: hypergeometric F-series, polyadic Liouville numbers.
Document Type: Article
UDC: 511.36
Language: Russian
Citation: E. Yu. Yudenkova, “Values of hypergeometric F-series at polyadic Liouvillea points”, Chebyshevskii Sb., 22:2 (2021), 536–542
Citation in format AMSBIB
\Bibitem{Yud21}
\by E.~Yu.~Yudenkova
\paper Values of hypergeometric $F$-series at polyadic Liouvillea points
\jour Chebyshevskii Sb.
\yr 2021
\vol 22
\issue 2
\pages 536--542
\mathnet{http://mi.mathnet.ru/cheb1053}
\crossref{https://doi.org/10.22405/2226-8383-2018-22-2-536--1}
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  • https://www.mathnet.ru/eng/cheb/v22/i2/p536
  • This publication is cited in the following 1 articles:
    1. V. G. Chirskii, “Polyadic Liouville numbers”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 137–141  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:97
    Full-text PDF :32
    References:19
     
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