I saw an integral question that involved the digamma function, which I know nothing about, and I want to learn more about it and its properties and other functions like Polylogarithm function and Hypergeometric function. So, I searched through all of my analysis books (Differential Equations, Real Analysis, Complex Analysis) to find any book that has the digamma function, but none of them mention it even once. The only books that contain the digamma function that I have are problem books, which assume that the reader is familiar with it and present hard problems involving it, so they are not useful for me. The other type is special functions books, which don’t contain any proofs, so they are also not useful.
I know that I can search for the Polygamma function on Wikipedia, but this is more about finding an analysis book that contains the Polygamma function and its properties because this book might have more interesting theories and functions that I didn’t know anything about like Polylogarithm function, Hypergeometric function or even functions and theorems that I didn't know they even existed before.
If there is no analysis books with these functions and the other types of books (problems books, special functions book) one can't rely only on them, then how did many people learn about these functions anyway?
So I want to ask for analysis books (Complex or Real but it would be better if it is a complex analysis book) that have Polygamma function, Polylogarithm function and Hypergeometric function and its properties with proofs also I am looking for rigorous books that doesn't contain any real-world application or physics.