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

DOI: 10.2140/pjm.1981.95.307

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