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| author | joshuab <> | 2010-06-30 20:33:46 +0000 | 
|---|---|---|
| committer | bnewbold <bnewbold@adelie.robocracy.org> | 2010-06-30 20:33:46 +0000 | 
| commit | 456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4 (patch) | |
| tree | f2b486379c0c49a5f35f511808b9f13aac06a273 | |
| parent | d893f7c5d6401b0f0f2121aca568303f44e11551 (diff) | |
| download | afterklein-wiki-456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4.tar.gz afterklein-wiki-456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4.zip | |
fixing numbering
| -rw-r--r-- | Problem Set 1.page | 14 | 
1 files changed, 7 insertions, 7 deletions
| diff --git a/Problem Set 1.page b/Problem Set 1.page index 5a109c8..8dc8694 100644 --- a/Problem Set 1.page +++ b/Problem Set 1.page @@ -19,11 +19,11 @@  -  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? | 
