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Diffstat (limited to 'Problem Set 1.page')
| -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? |