Re: qPochhammer symbol and indefinite products in general

[Joerg Arndt <arndt@jjj.de>]

Some of the files under http://jjj.de/pari/ might be useful.
Especially eta.gpi for computation of q-pochhammer.

Best regards,   Joerg Arndt


* E Y <ernestyalumni@gmail.com> [Mar 16. 2016 12:14]:
> qPochhammer symbol and indefinite products in general
> 
> Pari-users,
> 
> Hi, I’m Ernest Yeung, and I’m writing to the users list because I saw a question about the qPochhammer symbol for Pari/GP in the mailing list, but it was too old to reply to (I also joined the mailing list just now and so haven’t gotten used to interacting with the list; any advice on etiquette would help).  
> 
> Is there a way to implement the qPochhammer symbol in Pari/GP for arbitrary variables (i.e. an “indefinite product”, with variables in the ending number you multiply up to?)?  How would I implement such a symbol?  A function returning a function?  Any suggestions would help since I’m starting out.  
> 
> Ultimately, I’d want to implement this paper/algorithms for q-analogues of the Wilf-Zeilberger algorithm, for proving q-hypergeometric multisum identities:
> http://www.risc.jku.at/research/combinat/software/ergosum/RISC/qMultiSum.html
> but in Pari/GP because
> -I’ve used qMultiSum.m before, but there were serious slowdowns due to using Mathematica; would like to see speed up for my needs; hopefully Pari/GP based on C,C++ can help speed up computation
> -would like an open-source alternative so to develop directly for my needs in implementing q-hypergeometric summations
> 
> Any thoughts on implementing recursion algorithms of the such (Wilf-Zeilberger, Gosper’s algorithm, etc.), or even in general doing symbolic computation and writing scripts for Pari/GP AND how indefinite summation and INDEFINITE products (i.e. NOT specifying the bounds before with numbers) are to be implemented in Pari/GP would help.  Thanks, -Ernest Yeung
> 
>