On The Divergence in the General Sense of q-Continued Fractions on the Unit Circle

Authors

Douglas Bowman, Northern Illinois University
James McLaughlin, West Chester University of PennsylvaniaFollow

Document Type

Article

Publication Date

2003

Abstract

We show, for each q-continued fraction G(q) in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which G(q) diverges in the general sense. This class includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fraction. We discuss the implications of our theorems for the general convergence of other q-continued fractions, for example the G¨ollnitz-Gordon continued fraction, on the unit circle.

Publication Title

Communications in the Analytic Theory of Continued Fractions

Publisher

Colorado Mesa University

Volume

11

First Page

25

Last Page

49

Comments

Preprint version is available here.

Recommended Citation

Bowman, D., & McLaughlin, J. (2003). On The Divergence in the General Sense of q-Continued Fractions on the Unit Circle. Communications in the Analytic Theory of Continued Fractions, 11, 25-49. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/42