Is it appropriate to ask a professor for a discount on his expensive book?
Authors usually don't and cannot sell directly copies of their books, and the price is decided by the publisher.
Of course, an author has their draft copy in electronic format, but they might not even have the final electronic version as published. Authors typically receive a few courtesy copies of their books, but they have no access to other copies for free.
My suggestion however is to borrow the book from your university library: that's what library are for, after all.
If the library doesn't have a copy, depending on your position, you can:
- Suggest the library to buy a copy. Many university libraries buy books according to the suggestions of their faculties: if you cannot do this directly, probably your adviser can.
- Ask your library if they can loan it from another library. In many countries there is a system of interlibrary loans, and sometimes it works even across different countries.
I don't think it is rude to ask for the preprint of the book. In fact, many authors publish the preprint for books on arxiv(I can give examples of this). However, the rudeness depends on the culture and has many dependencies. Finally, you can use Libgen for downloading/uploading books, and many authors put their book also here, although they would not admit it.
I was in same situation and found that the author was on research gate. I message him about my financial constraints and politely asked for favor to which he replied with the copy of whole book.
I think you can also ask him, as they are well aware of student problems and might help you out. In case of refusal thank him and understand his position.