diff options
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? |