On Tue, Mar 15, 2016 at 12:14 AM, Subham Tibra <[email protected]> wrote: > Hi Ondrej, > Regarding the conversion of holonomic to hypergeometric, approaches I have > in mind: > > If the ratio of terms can be found out directly using the recurrence > relation then one can get the hypergeometric representation > Getting a closed form of the recurrence and thus computing the ratio to > convert to hypergeometric > Guessing the function from the coefficients in series expansions > > Are there any more methods which I am missing? As you wrote here
I think those are the main once, at least as far as I know. >> >> "To convert a holonomic function back to a hypergeometric one is also >> quite easy, as one can expand the holonomic function into a (formal) series, >> and then compute the ratio of terms and get the hypergeometric function out >> of it." > > > Does the ratio here means the numerical value? How one can get the > hypergeometric function from the numerical values of the ratio? Not the numerical value, but a symbolic value of the ratio. Once you have the ratio, then you factor the polynomial numerator and denominator and read off the hypergeometric coefficients. See e.g. here for details: http://www.theoretical-physics.net/dev/math/hyper.html > On Sunday, March 13, 2016 at 12:41:41 AM UTC+5:30, Subham Tibra wrote: >> >> I have few questions. >> >> When finding a recurrence relation for the series expansion, is it >> required just about the origin or at any arbitrary point? I am not sure about that. That's a good question. I would assume an arbitrary point, but perhaps not. >> >> In cases, when the ratio of terms can be found out directly by the >> recurrence relation or we can find the closed form of the recurrence, we can >> convert holonomic to hypergeometric. If these are not possible, then what >> would be our approach to convert to hypergeometric? If it's not possible, then we have to use other means, perhaps some kind of a pattern matching. A lot of functions can be written as a linear combination of hypergeometric functions, so I would concentrate on that. Ondrej >> >> On Friday, March 11, 2016 at 9:48:14 PM UTC+5:30, Subham Tibra wrote: >>> >>> Hi, I have created a pull request regarding this. Please give your >>> suggestions and ideas here. >>> >>> On Tuesday, March 8, 2016 at 10:17:24 PM UTC+5:30, Ondřej Čertík wrote: >>>> >>>> Hi Tabot, >>>> >>>> On Tue, Mar 8, 2016 at 4:59 AM, Tabot Kevin <[email protected]> wrote: >>>> > Hello Ondrej, I am really interested in this projects. Please can you >>>> > point >>>> > me to steps i can take to get started familiarizing myself with the >>>> > SymPy >>>> > environment for this project? >>>> >>>> The best is to try to figure out how the holonomic functions should be >>>> implemented, as discussed in this thread. >>>> >>>> Everyone --- if you are interested in this project, definitely >>>> consider applying. We accept the best proposals, and if two or more >>>> proposals are accepted for similar work, GSoC allows us to amend the >>>> work, so that you work complements each other. We've done it in the >>>> past, e.g. with regards to fast series expansion/polynomials. >>>> >>>> Ondrej > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/31238a9b-1830-4e47-86a6-5b5f1f44ede1%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CADDwiVB8KfRq8iyPfaBrdeB6xDN4R4cLGAZqnrDy0%3DF7JR-4rw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
