analytic relief, modulus surface
The geometric image of the modulus $|f(z)|$ of an analytic function $f(z)$, $z=x+iy$. The analytic "landschaft" of a function $f(z)$ is the surface over the $(x,y)$-plane with $z$-coordinate $|f(z)|$. An analytic "landschaft" sometimes provides a good illustration of the behaviour of specific functions. For the relief of the principal functions see .
|||A.I. Markushevich, "Theory of functions of a complex variable" , 1 , Chelsea (1977) pp. Chapt. 2 (Translated from Russian)|
|||E. Jahnke, F. Emde, "Tables of functions with formulae and curves" , Dover, reprint (1945) (Translated from German)|
Instead of the German word "Landschaft", the English "landscape" is also used.
Analytic landschaft. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Analytic_landschaft&oldid=33498