1
vote
1answer
107 views

$q$-differential equation for the Rodgers polynomials?

The Rodgers polynomials $C_{\alpha,q}$ are a particular family of well-known $q$-hypergeometric function. For example, a description can be found here on Wikipedia. For the special case of $q=1$, we ...
3
votes
1answer
493 views

Pochhammer symbol of a differential, and hypergeometric polynomials

I have a minor result which I'm sure has come up somewhere before but I can't seem to find it. Consider a confluent hypergeometric function of the form $$\newcommand{\ff}{{}_1F_1} ...
0
votes
1answer
436 views

The zeros of the digamma function

I wonder what work have been done on the zeros of the digamma function and on the values of the gamma function at such points (on the negative real axis). Any help please :)
9
votes
7answers
1k views

A good reference to grok hypergeometric functions?

When I was introduced during my degree to special functions, I made friends with a number of nice functions - Laguerre, Legendre, Hermite, Bessel, and whatnot - but I made only a passing acquaintance ...
7
votes
3answers
1k views

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 ...