On 3/13/12 5:29 AM, Noud wrote:
> On Tue, Mar 13, 2012 at 6:08 AM, Robert Dodier
> <robert.dodier at gmail.com <mailto:robert.dodier at gmail.com>> wrote:
>
> On 3/11/12, Noud <jwaixs at gmail.com <mailto:jwaixs at gmail.com>> wrote:
>
> > I tried to read the hypergeometric.lisp, but I could not make
> much of it.
> > Probably the biggest problem here is that I do not have a lot of
> experience
> > with Lisp, but I do also not really know how Maxima work. Is
> there more
> > documentation about how to implement new functions in Maxima? Or
> could you
> > give me some advice on how to proceed?
>
> Well, probably the way to go about this is for you to tell us a list
> of identities you want to put into play, and we'll try to advise
> you as
> to the best way to accomplish that. Maybe the best way is to write
> a Maxima function, or create a user-defined simplification rule,
> or something else. Maybe Lisp programming is needed, and maybe
> it isn't; no need to jump to conclusions just yet.
>
> best
>
> Robert Dodier
>
>
> There is this book Basic Hypergeometric Series from Gasper and Rahman,
> I basically want to implement the first chapter of this book.
You can't "implement an identity" generally. You have to decide
"if the simplifier sees XXX then it should replace it with YYY [under
some conditions]"
An identity doesn't say which way to transform.
There are papers to look at which attempt to meld the hypergeometric
function adjacency relations into
a goal-oriented simplifier. I don't know to what extent your series
ideas are the same as the HG function
issues, but there is literature to look at, as well as a person to
consult, Bill Gosper who has written about
some of these issues in terms of programming in Lisp and Macsyma.
.....
> The main identities and functions here are:
>
> (-) The q-binomial formula,
> (-) q-exponentials,
> (-) Heine's transformation formulas for 2_\phi_1,
> (-) Heine's q-analogue of Gauss' summation formula,
> (-) q-analogue of Saalschutz's summation formula,
> (-) Bailey-Daum summation formula,
> (-) q-Gamma and q-Beta functions
>
> Furthermore there are quite some identities spread through the first
> chapter and exercises which are very basic but important. Also I would
> like to have some q-analoges for orthogonal polynomials like the
> Little q-Jacobi polynomials, q-Hermite polynomials, etc.
>
> Best regards,
> Noud
>
>
>
>
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