This article is cited 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
$$ q_n=\sum_{j=1}^{k-1}p_{k-j,n}q_{n-j}, \qquad p_{1,n}\ne0, \quad n=0,1,\dots, $$
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.

UDC: 511.36+514.172.45

Received: 11.01.2003
Revised: 26.11.2004

DOI: 10.4213/mzm2661

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

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