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| -rw-r--r-- | Problem Set 3.page | 3 |
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diff --git a/Problem Set 3.page b/Problem Set 3.page index b1011b9..9504969 100644 --- a/Problem Set 3.page +++ b/Problem Set 3.page @@ -43,4 +43,7 @@ $$ f(z + 2\pi) = f(z) $$ $$ f(z + \tau) = f(z) $$ (Such a function is said to be doubly periodic). Show that $f$ is constant. Hint: Write down holomorphic Fourier series for $f(z)$ and $f(z+\tau)$, and compare their Fourier coefficients. +11. Compute the Fourier coefficients of the function $f(x) = \frac{1}{2} - \frac{x}{\pi}$ and use this to show that +$$ \sum_{n = 1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} $$ + # Solutions |