In this paper, we introduce a generalization of palindromic continued fractions as studied by Adamczewski and Bugeaud. 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. 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.
"Generalized palindromic continued fractions." Rocky Mountain J. Math. 48 (1) 219 - 236, 2018. https://doi.org/10.1216/RMJ-2018-48-1-219