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

[Christian Sievers]

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