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\title{A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent}
\author{Manuel Eberl}
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\begin{abstract}
In this article, I formalise a proof from THE BOOK~\cite[Chapter~23]{thebook}; namely a formula that was called `one of the most beautiful formulas involving elementary functions':
\[\pi \cot(\pi z) = \frac{1}{z} + \sum_{n=1}^\infty\left(\frac{1}{z+n} + \frac{1}{z-n}\right)\]
The proof uses Herglotz's trick to show the real case and analytic continuation for the complex case.
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