The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle

Abstract

We consider two classes of $q$-continued fraction whose odd and even parts are limit 1-periodic for $|q|>1$, and give theorems which guarantee the convergence of the continued fraction, or of its odd- and even parts, at points outside the unit circle.

9 pages. arXiv admin note: text overlap with arXiv:1812.10878

Cited by in corpus (2)

• A Theorem on Divergence in the General Sense for Continued Fractions
• On the Divergence in the General Sense of $q$-Continued Fraction on the Unit Circle