Vol. 95, No. 2, 1981

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ISSN: 0030-8730
A generalization of a classical necessary condition for convergence of continued fractions

Robert Heller and Francis Aubra Roach

Vol. 95 (1981), No. 2, 307–310
Abstract

One of the most frequently cited necessary conditions for convergence of continued fractions is the divergence of a particular series. In this paper, we show that convergence of a continued fraction implies divergence of each member of an infinite collection of series.

Mathematical Subject Classification 2000
Primary: 30B70
Milestones
Received: 6 September 1979
Published: 1 August 1981
Authors
Robert Heller
Francis Aubra Roach