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-rw-r--r--Problem Set 3.page8
1 files changed, 4 insertions, 4 deletions
diff --git a/Problem Set 3.page b/Problem Set 3.page
index 8f9876b..e5bac92 100644
--- a/Problem Set 3.page
+++ b/Problem Set 3.page
@@ -61,13 +61,13 @@ $$ \frac{\partial f}{\partial r} = \frac{\partial f}{\partial x}\frac{\partial x
together with the Cauchy-Riemann equations in rectangular coordinates.
8. By applying Cauchy-Riemann equations in polar coordinates to a Fourier series
-\[ f(r,\theta) = \sum_{n = -\infty}^{\infty} a_n(r) e^{in \theta} \]
+$$ f(r,\theta) = \sum_{n = -\infty}^{\infty} a_n(r) e^{in \theta} $$
you should obtain the following system of ordinary differential equations for the coefficients $a_n(r)$:
-\[ \frac{d a_n}{dr} = \frac{na_n}{r} \]
+$$ \frac{d a_n}{dr} = \frac{na_n}{r} $$
Write this in the form
-\[ \frac{d a_n}{a_n} = \frac{n dr}{r} \]
+$$ \frac{d a_n}{a_n} = \frac{n dr}{r} $$
and integrate to get the solution. Then write
-\[ z = re^{i\theta} \]
+$$ z = re^{i\theta} $$
to derive the Laurent series.
# Solutions \ No newline at end of file