View source for Analytic landschaft

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''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 [[#References|[2]]].

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.I. Markushevich,   "Theory of functions of a complex variable" , '''1''' , Chelsea  (1977)  pp. Chapt. 2  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E. Jahnke,   F. Emde,   "Tables of functions with formulae and curves" , Dover, reprint  (1945)  (Translated from German)</TD></TR></table>



====Comments====
Instead of the German word  "Landschaft", the English "landscape" is also used.