Recent work on hypergeometric functions Does anyone know of a monograph/survey on the modern history of (basic or elliptic) hypergeometric functions and their applications?
I haven't had much time to search the literature, and because it is summer it is hard to reach professors or specialists, which is why I am asking the question here. It is also likely that there are obvious choices out there that I am unaware of because of my ignorance in the field. I would appreciate it a lot if along with the suggestions you could give a quick description of what the book/article treats.
 A: Gjergji, there are remarkable articles by Richard Askey:
(1) "Ramanujan and hypergeometric and basic hypergeometric series"
in
Russian
Math. Surveys 45:1 (1990) 37--86;
reprinted in Ramanujan: essays and surveys, Hist. Math. 22 
Amer. Math. Soc., Providence, RI, 2001, pp. 277--324;
(2) "A look at the Bateman project" 
in The mathematical legacy of Wilhelm Magnus: groups, geometry
and special functions (Brooklyn, NY, 1992), 29--43,
Contemp. Math. 169, Amer. Math. Soc., Providence, RI, 1994.
(I asked Dick exactly this question, maybe without accenting on "modern theory",
some years ago.) The modern theory is mostly multiple hypergeometric functions
related to root systems; for a nice survey on the roots of these functions,
the Selberg integral, see
(3) P. Forrester and S.O. Warnaar,
"The importance of the Selberg integral",
Bull. Amer. Math. Soc. (N.S.) 45:4  (2008) 489--534.
Elliptic functions are hypergeometric functions of the 21st century:
(4) V.P. Spiridonov, 
"Essays on the theory of elliptic hypergeometric functions",
Russian Math. Surveys 63:3 (2008) 405--472.
A: "Basic Hypergeometric Series" 2nd Edition, George Gasper and Mizan Rahman, ISBN: 0521833574 would be a good place to start. Chapters 9-11 of the second edition are new and deal with:


*

*Linear and bilinear generating functions for basic orthogonal polynomials; 

*q-series in two or more variables; 

*Elliptic, modular, and theta hypergeometric series

A: Hyper Geometric Functions, My Love: Modular Interpretations of Configuration Spaces (Aspects of Mathematics) by Masaaki Yoshida 
Discriminants, Resultants, and Multidimensional Determinants 
Israel M. Gelfand, Mikhail Kapranov, Andrei Zelevinsky 
I heard a talk by Rivoal a decade back when he had just had his breakthrough concerning irrationality of zeta values.  He quoted some very classical but not well-known results and got asked where he learned them.  He recommended this book:
Confluent Hypergeometric Functions  L. J. Slater 
