Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Divergence of continued fractions related to hypergeometric series

Author: Lisa Lorentzen
Journal: Math. Comp. 62 (1994), 671-686
MSC: Primary 40A15; Secondary 33C05
MathSciNet review: 1203736
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ K({a_n}/{b_n})$ be a limit periodic continued fraction of elliptic type; i.e., $ {a_n} \to a$ and $ {b_n} \to b$, where $ a/(b + w)$ is an elliptic linear fractional transformation of w. We show that if $ \sum {\vert{a_n} - a\vert < \infty } $ and $ \sum {\vert{b_n} - b\vert < \infty } $, then $ K({a_n}/{b_n})$ diverges. This generalizes the well-known Stern-Stolz Theorem. The Gauss continued fraction (related to hypergeometric functions) is used as an example. We also give an example where $ {a_n} - a = \mathcal{O}({n^{ - 1}})$ and $ {b_n} = b = 1$ and $ K({a_n}/{b_n})$ converges. The divergence result is also generalized further.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 40A15, 33C05

Retrieve articles in all journals with MSC: 40A15, 33C05

Additional Information

PII: S 0025-5718(1994)1203736-3
Keywords: Hypergeometric series, divergence of continued fractions
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia