From 456019ea32b16bd7b7cbd2d0f271a918f0ab6aa4 Mon Sep 17 00:00:00 2001 From: joshuab <> Date: Wed, 30 Jun 2010 20:33:46 +0000 Subject: fixing numbering --- Problem Set 1.page | 14 +++++++------- 1 file 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? -- cgit v1.2.3