Tridimensional display of the Z=Gamma(Z) iteration inside [-20.0,+20.0]x[-20.0,+20.0] (bird's-eye view) [Visualisation tridimensionnelle de l'itération Z=Gamma(Z) 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 iteration of the Gamma function:
```                    Z  = C (current point)
0

Z  = Gamma(Z   )
n          n-1
```

(for each Z(0) inside a subset of the complex plane) as a surface in a tridimensional space (the two dimensions of the complex plane plus the number of iterations). The argument of the last computed Z(n) 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 iteration of the Gamma function:

• the number of irerations alone,
• the argument alone.

(CMAP28 WWW site: this page was created on 03/17/2000 and last updated on 03/04/2019 12:36:37 -CET-)

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