Correct me if I am wrong, then the coefficient ( constant / polynomial) of
the i'th series coefficient in the recurrence relation must be Sum_{ j }
A(i, j)*x^j
in the context of Ondrej's write
up https://gist.github.com/certik/847cafaf3111730c5b3f .
On Wednesday, February 24, 2016 at 8:41:43 PM UTC+5:30, Ralf Stephan wrote:
>
> On Wednesday, February 24, 2016 at 3:59:08 PM UTC+1, shubham tibra wrote:
>>
>> And regarding the conversion of Holonomic to Hypergeometric function, we
>> need to expand the holonomic function to a power series. How we can do that
>> without having the actual symbolic representation of the function?
>>
>
> Series coefficients of holonomic functions satisfy linear recurrences
> (with constant
> and polynomial coefficients). It follows that the series coeffs can be
> represented
> as formal sums, and equalities of different formal sums can be decided by
> comparing
> the underlying holonomic function (so you can prove hypergeometric sum
> equalities).
> See e.g. papers by Zeilberger for applications of this fascinating
> subject.
>
>
>> How we will handle the special cases when the Holonomic function
>> represents an elementary function or a polynomial?
>>
> They have hypergeometric representations as well as far as I recall.
>
> Best,
>
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