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.



Recent work on hypergeometric functions
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](http://dx.doi.org/10.1070/RM1990v045n01ABEH002325);
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.](http://dx.doi.org/10.1090/S0273-0979-08-01221-4)


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.](http://dx.doi.org/10.1070/RM2008v063n03ABEH004533)


