Tridimensional display of the Gamma function inside [-20.0,+20.0]x[-20.0,+20.0] [Visualisation tridimensionnelle de la fonction Gamma dans [-20.0,+20.0]x[-20.0,+20.0]].

The Gamma function can be computed for all z with the following analytic continuation:
                    Gamma(z) = factorial(z-1)

                                              1                log(2 ||)
                    log(factorial(z)) = (z + ---)log(z) - z + ------------
                                              2                    2

                                        \             B
                                         \             2k
                                      +  /      ---------------
                                        /______           2k-1

                                      + epsilon(z,N,V)

                    factorial(z) = --------------------

This picture displays the modulus of the Gamma function as a surface in a tridimensional space (the two dimensions of the complex plane plus the modulus). The so-called phase of the Gamma function (its argument) is displayed as colors painting the surface; the [0, 2.pi] segment is mapped on the {Blue,Red,Magenta,Green,Cyan,Yellow,White} set.

Here are more pictures about the Gamma function:

(CMAP28 WWW site: this page was created on 06/25/1999 and last updated on 09/15/2022 19:01:52 -CEST-)

[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related NumberTheory picture gallery [Visitez la galerie d'images NumberTheory associée]]

[Go back to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]

[The Y2K Bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]

Copyright © Jean-François Colonna, 1999-2022.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 1999-2022.