Talk:Q-series

I don't know a lot about q-series, but it seems a bit confusing that we say they are the q-analog of a factorial, but that we say that q-analog are the q-series version of something.


 * I agree. The intro is too compressed - should mention some general idea first, such as that q-analogues are certain useful extrapolations from objects known in combinatorics. Charles Matthews 14:13, 8 August 2006 (UTC)

That's not a q-series!
This article is badly named. What this article is describing is a "q-Pochhammer symbol", or as the article says, a "q-shifted factorial"; a q-series is in fact a sum (a.k.a., series) in which the coefficients can be expressed using q-Pochhammer symbols. This article and MathWorld are the only places I've ever seen them called "q-series"; is there a primary source for this terminology? My guess is that at some point somebody was confused by the existence of a q-series expansion for the q-Pochhammer symbol. A decent online reference for such things is http://fa.its.tudelft.nl/~koekoek/askey/contents.html; a better (but offline) reference is Gasper and Rahman's book "Basic hypergeometric series", which discusses the main type of q-series, the basic hypergeometric series. (The Wikipedia article on basic hypergeometric series specifically mentions the alternate name of hypergeometric q-series, which is nonsense per the current article on q-series!)

The upshot is that this page should be renamed either Q-Pochhammer symbol or Q-shifted factorial (the latter is currently a redirect to here), and be rewritten accordingly (a search-and-replace, essentially), and Q-series should probably redirect to basic hypergeometric series until such point as more general content is written. I'd be bold, but I've no idea how to move an article without breaking history. 209.125.235.244 15:54, 12 April 2007 (UTC)

Since nobody's done anything, I've made the changes to this page to make it completely ready for a move to q-Pochhammer symbol; since Pochhammer symbol exists, but shifted factorial does not, it would seem that q-shifted factorial is the one that should be a redirect. I'm not completely happy with the definition I've put in for q-series (and I'm not sure if it really belongs in this article, or in a stub of its own in this location), but I haven't actually been able to track down any reliable reference that defines the word "q-series"; it's always more of an "I know one when I see one" thing. Possibly George Andrews' book (the one with "q-series" in the title) will have a suitable definition. I've also gone through "What links here" to change fix the incorrect uses of "q-series" that have propagated. 209.125.235.244 19:33, 26 April 2007 (UTC)

Just pointing out that the above applies to the version of the page that has now been moved to q-Pochhammer symbol (Thanks, Greg!). 209.125.235.244 14:58, 10 May 2007 (UTC)


 * Uhh, I strongly disagree with the above assesment. I wrote the orignal draft of both this article and the articles on the basic hypergeometric series, and the other hypergeometric series articles. A review of the literature, from the classic cases of Ramanujan and hypergeometric series, up to modern applications in statistical mechanics and chaos, viz. the Yang-Baxter equations, in quantum Lie algebras and quantum Lie groups, uses a consistent notion of a q-series as that which was originally used in this article, and as given in Mathworld. See, for example Jurgen Fuchs, "Affine Lie Algebras and Quantum Groups" Cambridge, or Chari, Pressley, "A guide to Quantum Groups", Cambridge. However, since the structure of this article was wrecked, and I rather don't have the time to fix anything, I will just make it a redirect for now. linas 16:52, 10 November 2007 (UTC)