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

[Neil Sloane]

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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