[seqfan] Re: A063747 sign of power series expansion of the Gamma function

[Hugo Pfoertner]

Why not use the result of Michel Marcus's new PARI program? Is there any
doubt that PARI can calculate e.g. 100 terms correctly? Then we have a very
fundamental problem.


On Fri, May 19, 2023 at 9:34 PM Sean A. Irvine <sairvin at gmail.com> wrote:

> Yes, I will make an update.
>
> Thank you Jean-François and Brendan for taking the time to verify.
>
> Sean.
>
>
>
> On Sat, 20 May 2023 at 07:04, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Well, if a(46) is wrong (which seems to be the case), could someone
> please
> > make the correction?  And probably all the terms after a(46) should be
> > deleted, and we should give it keyword "more".
> >
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, Chairman, OEIS Foundation.
> > Also Visiting Scientist, Math. Dept., Rutgers University,
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Fri, May 19, 2023 at 3:14 AM Jean-François Alcover <
> > jf.alcover at gmail.com>
> > wrote:
> >
> > > Mma's SeriesCoefficient[1/Gamma[1 - x], {x, 0, n}] // Sign gives -1 for
> > > n=46 (after 15 mn !)
> > >
> > > Le ven. 19 mai 2023 à 06:52, Brendan McKay via SeqFan <
> > > seqfan at list.seqfan.eu>
> > > a écrit :
> > >
> > > > My typo, it is e-38.  Oops.  B/
> > > >
> > > > On 19/5/2023 1:11 pm, Allan Wechsler wrote:
> > > > > One of you said "e-38" and the other said "e-58". Do you really
> have
> > > > > 20 orders of magnitude of disagreement?
> > > > >
> > > > > On Thu, May 18, 2023 at 11:07 PM Brendan McKay via SeqFan
> > > > > <seqfan at list.seqfan.eu> wrote:
> > > > >
> > > > >     I also get -0.444..e-58  * x^46 in Maple using 60 digits.  The
> > > > >     calculation
> > > > >     is numerically unstable though.
> > > > >
> > > > >     B/
> > > > >
> > > > >     On 19/5/2023 12:31 pm, Sean A. Irvine wrote:
> > > > >     > Hi,
> > > > >     >
> > > > >     > I believe the terms in A063747 are incorrect for n>=46.
> > > > >     >
> > > > >     > https://oeis.org/A063747
> > > > >     >
> > > > >     > My attempts to reproduce the calculation in Maple and using
> > > > >     constructible
> > > > >     > reals in Java both yield a coefficient, like -0.44458...e-38
> *
> > > > >     x^46, from
> > > > >     > which a(46) should be -1 rather than 1.
> > > > >     >
> > > > >     > Is someone able to make an independent check?
> > > > >     >
> > > > >     > I was unable to run the existing Pari program beyond n=15,
> but
> > I
> > > > >     assume
> > > > >     > there is some way to tell Pari to try harder?
> > > > >     >
> > > > >     > (I previously emailed the author of the sequence, but
> received
> > > > >     no response.)
> > > > >     >
> > > > >     > Sean.
> > > > >     >
> > > > >     > --
> > > > >     > Seqfan Mailing list - http://list.seqfan.eu/
> > > > >
> > > > >
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