# Analytic landschaft

From Encyclopedia of Mathematics

*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].

#### References

[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) |

#### Comments

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

**How to Cite This Entry:**

Analytic landschaft.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Analytic_landschaft&oldid=33498

This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article