Re: [Axiom-developer] 20080221.01.tpd.patch (7099: complex gamma function investigation)

[root]

>> 
>> fixed 7099: complex Gamma bug
>> 
>> Note that at the value 1.0+4.6i there is a radical departure between
>> the table and the computed values in the imaginary part of the value
>> even though the real part is exact.
>
>(11) -> Gamma(1. + 4.5*%i)
>
>   (11)  - 0.004501804477919395 + 4.8078797963506284e-4 %i
>                                                    Type: Complex DoubleFloat
>(12) -> Gamma(1. + 4.6*%i)
>
>   (12)  - 0.0039079873004091254 - 1.7801308638883733e-4 %i
>                                                    Type: Complex DoubleFloat
>
>So, value of Gamma crossed brunch cut of logarithm and we have jump
>in numeric value by -2Pi.  However, the formulas in texbooks (including
>Abramowitz and Stegun) do not use numeric logarithm: log(Gamma(z))
>in texbooks is a holomrphic function for Re z > 0, in particular
>texbook log(Gamma(z)) is continouos, while numeric one have jumps.

The question is whether we want the numeric results to be
continuous. What's your opinion?

Tim