Generalized palindromic continued fractions

In this paper, we introduce a generalization of palindromic continued fractions as studied by Adam-czewski and Bugeaud [2]. We refer to these generalized palindromes as m-palindromes, where m ranges over the positive integers. We provide a simple transcendency criterion for m-palindromes, extending and slightly refining an analogous result of Adamczewski and Bugeaud [2]. We also provide methods for constructing examples of m-palindromes. Such examples allow us to illustrate our transcendency criterion and to explore the relationship between m-palindromes and stammering continued fractions, another concept introduced by Adamczewski and Bugeaud.