[seqfan] Re: A063747 sign of power series expansion of the Gamma function
Christian Sievers
seqfan at duvers.de
Fri May 19 07:42:05 CEST 2023
On Fri, May 19, 2023 at 02:31:10PM +1200, 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?
The O-Term needs to be in the argument to gamma.
With that we get the result of one.
But with a higher precision, PARI confirms your result:
? \p60
realprecision = 77 significant digits (60 digits displayed)
? polcoef(1/gamma(1-x+O(x^47)),46)
%1 = -4.445829736550756882101590352124643637411455901975243651454 E-39
(polcoeff is deprecated in favour of polcoef.)
All the best,
Christian
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