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 [2].


[1] A.I. Markushevich, "Theory of functions of a complex variable" , 1 , Chelsea (1977) pp. Chapt. 2 (Translated from Russian)
[2] 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.

How to Cite This Entry:
Analytic landschaft. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article