Am Dienstag, den 09.12.2008, 18:40 +0100 schrieb Dieter Kaiser:
> Am Montag, den 08.12.2008, 16:43 -0800 schrieb Edwin Woollett:
>
> > and the differences:
> >
> > (%i10) %o9 - %o8;
> > (%o10) [8.0491169285323849E-15-5.5511151231257827E-17*%i,
> > 2.2204460492503131E-16*%i+7.6605388699135801E-15,
> > 2.5424107263916085E-14-3.6082248300317588E-15*%i,
> > 5.8352933596239609E-11*%i+4.1387115956581511E-11,
> > 1.9600563649913028E-7*%i+2.5509862389139215E-7,
> > 0.016804536220479*%i-0.0089949769040033,
> > -7101.770897795603*%i-2016.743759694998]
>
> You have found a bug. I needed some time to get the reason for the wrong
> calculation, but there is a range of values where we get wrong results
> for a negative realpart of a complex number.
I have found the reason. Unfortunately, it is an problem with the
numerical routines of the Incomplete Gamma function.
In this example we have to calculate gamma_incomplete(0.5,z^2) with a
pure imaginary argument. For this argument a series expansion is done.
This expansion converge for a pure imaginary value to a wrong result.
For a pure imaginary less than about 10 the error in the series is very
small, but grows very fast with increasing argument.
We get the wrong result for a bigfloat calculation too. Perhaps we can
improve the series expansion for a pure imaginary argument or do the
calculation in another way.
Dieter Kaiser