>> >> 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 _______________________________________________ Axiom-developer mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-developer
