The phrase "study at specious" can have various synonyms depending on the context. If one is referring to examining or analyzing something that appears to be false, then synonyms can include scrutinize, investigate, or examine. On the other hand, if one is referring to studying in a dubious or deceitful atmosphere, then words like analyze, review, or investigate can be used. In a more general sense, synonyms for studying can include learning, researching, exploring, or delving into a subject. Ultimately, the choice of synonyms depends on the desired tone, level of formality, and the specific nuances of the context.