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
>
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