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## Re: [Axiom-developer] 20080221.01.tpd.patch (7099: complex gamma functio

**From**: |
root |

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

**Date**: |
Thu, 21 Feb 2008 21:57:07 -0500 |

>*> *
>*> 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