[seqfan] Re: Integer Sequence Analysis in Mathematica 7
Alexander Povolotsky
apovolot at gmail.com
Sat Nov 22 02:59:07 CET 2008
Dear Maximilian,
PURRS is not using points, it is ONLY using the recurrence formula -
check it out yourself
Regards,
ARP
On Fri, Nov 21, 2008 at 8:54 PM, Maximilian Hasler
<maximilian.hasler at gmail.com> wrote:
> Well, for 30 given values there's always a polynomial of degree 29
> that fits *exactly* through these points, but in general not through
> the 31st point...
> Did you try to ask for the "exact" solution for 15 points and then to
> check the 16th point ?
> (NB: I don't pretend that what you copied is a polynomial !)
>
> But I agree that HypergeometricPFQ is a nice "encoding" of the answer.
> Well, actually A001609(n) is the most concise and most informative way
> to code that function.
>
> Maximilian
>
>
> On Fri, Nov 21, 2008 at 9:45 PM, Alexander Povolotsky
> <apovolot at gmail.com> wrote:
>> Dear Maximilian,
>>
>> I was not talking ggf, I meant closed form analytical formula
>>
>> For example PURRS (The Parma University's Recurrence Relation Solver)
>> http://www.cs.unipr.it/purrs/ yields the following:
>>
>> Exact solution for x(n) = x(-1+n)+x(-3+n)
>> x(n) = 1/2*(I*(29/54+1/18*sqrt(93))^(1/3)*sqrt(3)-I*sqrt(3)*(29/54-1/18*sqrt(93))^
>> ...*(29/54-1/18*sqrt(93))^(1/3))^n*x(0)
>> for each n >= 0
>>
>> But when trying to add initial conditions for exact solution PURRS demo gives
>> PURRS Demo Error
>> memory limit exceeded
>>
>
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