Generalized Palindromic Continued Fractions
David M. Freeman

TL;DR
This paper generalizes the concept of palindromic continued fractions to m-palindromes, providing a transcendence criterion, construction methods, and exploring their relationship with stammering continued fractions.
Contribution
It introduces m-palindromes as a new generalization, extends transcendence criteria, and offers construction techniques and connections to stammering continued fractions.
Findings
Established a transcendence criterion for m-palindromes.
Developed methods to construct examples of m-palindromes.
Explored the relationship between m-palindromes and stammering continued fractions.
Abstract
In this paper we introduce a generalization of palindromic continued fractions as studied by Adamczewski and Bugeaud. We refer to these generalized palindromes as -palindromes, where ranges over the positive integers. We provide a simple transcendence criterion for -palindromes, extending and slightly refining an analogous result of Adamczewski and Bugeaud. We also provide methods for constructing examples of -palindromes. Such examples allow us to illustrate our transcendence criterion and to explore the relationship between -palindromes and stammering continued fractions, another concept introduced by Adamczewski and Bugeaud.
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