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

[Sean A. Irvine]

Hi,

Thanks to everyone who replied on this topic.  It generated a much more
lively discussion than I was expecting.

I've added, just now, a little more commentary to the sequence:

https://oeis.org/draft/A063747

Sean.


On Mon, 22 May 2023 at 02:51, Christian Sievers <seqfan at duvers.de> wrote:

>
> On Sun, May 21, 2023 at 04:19:20PM +1000, Brendan McKay via SeqFan wrote:
>
> > Your value:
> > -4.44582 97365 50756 88210 15903 52124 64363 74114 55901 97524 36514 54
> E-39
> > Correct value:
> > -4.44582 97365 50756 88210 15903 52124 64363 74014 36685 74871 82886 70
> E-39
> >
> > I.e., only 38 digits are correct.
>
> That's not surprising: we knew that with default precision PARI was
> completely off. I only wanted to show that it too gets someting about
> -4.4458 E-39.
>
> The flint library gets the same number as you do:
>
> >>> from flint import *
> >>> ctx.cap=100 # compute this many terms of the series
> >>> showgood(lambda: arb_series([1,-1]).rgamma().coeffs()[46],dps=58)
> -4.445829736550756882101590352124643637401436685748718288670e-39
>
>
> All the best,
> Christian
>
>
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