Difference between revisions of "Analytic landschaft"
From Encyclopedia of Mathematics
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| − | The geometric image of the modulus | + | 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]]]. |
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| − | Instead of the German word "Landschaft" , the English | + | Instead of the German word "Landschaft" , the English "landscape" is also used. |
Revision as of 11:15, 5 October 2014
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=33497
Analytic landschaft. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Analytic_landschaft&oldid=33497
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article