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- Title
A Generalization of Pincherle's Theorem to k-Term Recursion Relations.
- Authors
Parusnikov, V. I.
- 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 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.
- Subjects
RECURSION theory; MATHEMATICAL logic; INFINITE processes; RATIONAL numbers; INFINITY (Mathematics)
- Publication
Mathematical Notes, 2005, Vol 78, Issue 5/6, p827
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0188-7