TITLE: Reference Book on Special Functions
QUESTION [13 upvotes]: Now I'm studying the topic that uses the special functions frequently, so I find myself in need for some good reference book on the properties and equalities of the special functions. The optimal one might be the book with dictionary-like or handbook type lists of the properties of the special functions with sufficient amount of proofs. There are many books about the special functions but most of them are lack of proofs, or too pedagogically descriptive textbooks. I would rather prefer the book that I can search up the identities fast and can understand why does the equality hold at least briefly. Is there any good book that meets this condition?

REPLY [4 votes]: A book I really appreciated is
Lebedev - Special function and their applications 
Dove edition.