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Mat. Zametki, 2005, Volume 78, Issue 6, Pages 892–906 (Mi mz2661)  

This article is cited in 3 scientific papers (total in 3 papers)

A Generalization of Pincherle's Theorem to $k$-Term Recursion Relations

V. I. Parusnikov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: In 1894, Pincherle proved a theorem relating the existence of a minimal solution of three-term recursion relations to the convergence of a continued fraction. The present paper deals with solutions of an infinite system
$$ q_n=\sum_{j=1}^{k-1}p_{k-j,n}q_{n-j}, \qquad p_{1,n}\ne0, \quad n=0,1,…, $$
of $k$-term recursion relations with coefficients in a field $F$. We study the connection between such relations and multidimensional ($(k-2)$-dimensional) continued fractions. A multidimensional analog of Pincherle's theorem is established.

DOI: https://doi.org/10.4213/mzm2661

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English version:
Mathematical Notes, 2005, 78:6, 827–840

Bibliographic databases:

UDC: 511.36+514.172.45
Received: 11.01.2003
Revised: 26.11.2004

Citation: V. I. Parusnikov, “A Generalization of Pincherle's Theorem to $k$-Term Recursion Relations”, Mat. Zametki, 78:6 (2005), 892–906; Math. Notes, 78:6 (2005), 827–840

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Parusnikov V. I., “Continued fractions to the nearest even number”, Dokl. Math., 80:3 (2009), 867–871  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. Janiszewski S., “Perturbations of Moving Membranes in AdS(7)”, J. High Energy Phys., 2012, no. 9, 093  crossref  mathscinet  isi  elib  scopus  scopus
    3. Janiszewski S., Kaminski M., “Quasinormal Modes of Magnetic and Electric Black Branes Versus Far From Equilibrium Anisotropic Fluids”, Phys. Rev. D, 93:2 (2016), 025006  crossref  mathscinet  isi  scopus  scopus
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