Final answer:
Talcott Parsons is the most influential sociologist in the development of the functionalist perspective, which focuses on the interconnections and contributions of society's parts to overall stability.
Step-by-step explanation:
The theorist most influential in the development of the functionalist perspective in sociology is Talcott Parsons. While other sociologists like Émile Durkheim laid the groundwork for what would become functionalism, it was Parsons who further developed this approach into a comprehensive theory during the mid-20th century. Functionalism focuses on how the various parts of society contribute to the overall stability and functionality of the whole, and Parsons' work greatly expanded on how these parts are interconnected and how they contribute to social order.