Tridimensional display of the Gamma function inside (-20.0,20.0)x(-20.0,20.0) (bird's-eye view) [Visualisation tridimensionnelle de la fonction Gamma dans (-20.0,20.0)x(-20.0,20.0) (vue aérienne)].




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

                                          k=V
                                        _______
                                        \             B
                                         \             2k
                                      +  /      ---------------
                                        /______           2k-1
                                                 2k(2k-1)z
                                          k=1

                                      + epsilon(z,N,V)


                                      factorial(z+n)
                    factorial(z) = --------------------
                                    (z+1)(z+2)...(z+n)


This picture displays the logarithm of the modulus of the Gamma function as a surface in a tridimensional space (the two dimensions of the complex plane plus the logarithm of 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:





(this picture was created on 06/25/1999)
(this page -belonging to the CMAP28 site- was last updated on 03/09/2010 20:12:40 -CET-)


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