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authorjoshuab <>2010-06-30 20:33:46 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-06-30 20:33:46 +0000
commit456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4 (patch)
treef2b486379c0c49a5f35f511808b9f13aac06a273
parentd893f7c5d6401b0f0f2121aca568303f44e11551 (diff)
downloadafterklein-wiki-456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4.tar.gz
afterklein-wiki-456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4.zip
fixing numbering
-rw-r--r--Problem Set 1.page14
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- Show that the product of two holomorphic functions is holomorphic.
- Try to extend the following functions of a real variable to holomorphic functions defined on the entire complex plane. Is it always possible to do so? What goes wrong?
- a. $\sinh(z), \cosh(z)$
- - $\frac{z^3}{1 + z^2}$
- - $\sin(z), \cos(z)$
- - $\sqrt{z}$
- - $\log z$
- - $\mathrm{erf}(z)$, the antiderivative of the gaussian $e^{-z^2/2}$
- - $e^{1/z}$
+ a. $\sinh(z), \cosh(z)$
+ - $\frac{z^3}{1 + z^2}$
+ - $\sin(z), \cos(z)$
+ - $\sqrt{z}$
+ - $\log z$
+ - $\mathrm{erf}(z)$, the antiderivative of the gaussian $e^{-z^2/2}$
+ - $e^{1/z}$
What is the growth rate of the magnitude of these functions as $z \to \infty$ along the real axis? The imaginary axis? How does the argument change?