There are many synonyms for the phrase "study at accidental" that can be used to convey the same concept. Some of the most common alternatives include "study by happenstance," "study coincidentally," "study unexpectedly," "study fortuitously," and "study serendipitously." All of these phrases suggest that the act of studying occurred by chance or accident rather than as a deliberate choice. They can be used to describe situations where individuals unexpectedly encountered information or were exposed to a topic that they had not intentionally set out to study. Overall, there are many ways to convey the idea of studying accidentally, depending on the context and tone of the writing.