As a Senior Business Analyst (BA) with over two decades of experience as BA (did a little PM work, but prefer being a BA, is my passion), I can tell you that the only one responsible for gathering business requirements specifications is the BA (and that means Functional, Non-Functional, and Technical Specifications, including Use Cases, Flow Charts, etc.). The BA prepares a Business Requirement Document (BRD) and needs to be approved by the client, to ensure that all his/her needs are being met.
It is true, the requirements start with the client, as they are the ones in need of a solution to their current situation, however, the client does not speak technical and technical does not speak business, thus, the bridge is the Business Analyst. S/he has the skills needed to speak both languages, and collect all requirements, negotiate requirements, and come out with a recommended solution (or multiple solutions) from which the client will choose.
In the BRD, all information (not just requirements) must exist (Use Cases, Diagrams, specially flow charts, etc.). This is to ensure that when the solution is implemented there will be no gaps and it is the appropriate solution the client needs and to ensure that it is built with strong scalability to continue to improve it as time goes on.