A new proof of a theorem of Tietze

TL;DR

This paper presents a novel proof of Tietze's theorem concerning the convergence properties of infinite semi-regular continued fractions, offering new insights into their mathematical behavior.

Contribution

The authors introduce a new proof technique for Tietze's theorem, enhancing understanding of convergence in semi-regular continued fractions.

Findings

New proof of Tietze's theorem established

Improved understanding of convergence criteria

Potential applications in continued fraction analysis

Abstract

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.