Abelian Functions : Abel's Theorem and the Allied Theory of Theta Functions (Cambridge Mathematical Library)

Rating:
Summary: A precious jewel !
Review: When I was a Ph.D. student and had some problems finding suitable functions in order to study the multiloop scattering of strings, I found this rarity of a book. Although it was first published a long time ago (1897) it is probably one of the most complete works on complex functions of many variables and particularly on theta functions of many variables. In this book you can find some material that is not in any other book I know of, and the style makes it relatively easy to read.

It covers a large number of subjects, like Abel's theorem, abelian integrals of the first and second type, Riemann's theta functions, hyperelliptic (many variables) theta functions, radical and factorial functions, Jacobian functions, and degenerate abelian integrals.

I consider it a jewel among the books that cover the same subject, both for its completenes and its writing style.