When you look into scientific or popuplar science books, there are often acknowledgements listing all the people that where of "invaluable help", offered feedback, helped with editing the book, or provided information. Sometimes this kind of help is extensive, and yet these people are not listed as authors, because they did not write the book, and they do not receive a share of the sales.
One scholar providing information, discussion, and feedback on the content of the book of another scholar is usually done voluntarily and without compensation. It is part of the social life of a scientific community. This kind of help is usually but not always acknowledged in the acknowledgements.
Editing, research, sometimes even writing up small research papers which the book's author can process into sections of his book, is usually done by students who work as research assistants for the professor (in his capacity as a university teacher). These research assistants receive monetary compensation from the university at which they are employed. This kind of help is often but not always acknowledged in the acknowledgements.
If you are asked to help shape the basic outline of the book and/or write part of the final publication, you are a co-author and should be listed as such.
Not all scholarly publications are paid. Professors are paid by their universities, and their publications are considered part of their job. Scientific journals never pay for the research they publish, and scientific monographs often have small print runs that barely provide any income to the publishers at all. Only popular science books are commonly paid for. So whether being a co-author comes with any money will depend on what you publish and where.
These are the three options – feedback and information from one scholar to another, research assistant, and co-author – and when you write that "we don't know in what capacity" you are going to work with him and that you "will begin with meeting ... and my response to what he's written and perhaps extending his analysis", this sounds to me as if your next few meetings and the work you do in between them are meant to find out how you may work together and clarify your status.
"[E]xtending his analysis" would be the work of a co-author, while "response to what he's written" sounds like free feedback (and a mention in the acknowledgements). "[S]cholarship and analysis" could both be the work of a paid research assistant (mentioned in the acknowledgements) and a co-author.
If you get the impression that you are going to be doing the groundwork as an assistant for your professor's publication, don't hesitate to ask for employment and remuneration. Whether or not he mentions you in the acknowledgements is up to him. You can ask for it, but not demand it, although not mentioning you would be extremely rude.
If you are given equal status and influence on the content and you agree that you will be writing or cowriting (parts of) the book, ask him directly about this, if he doesn't mention it himself. Consider asking another question on Academia.SE then, about how this kind of cooperation is usually done, whether there is a contract or just a spoken agreement, etc.
