A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent

Manuel Eberl 🌐

March 15, 2022

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Abstract

In this article, I formalise a proof from THE BOOK; namely a formula that was called ‘one of the most beautiful formulas involving elementary functions’:

πcot(πz)=1z+n=1(1z+n+1zn)

The proof uses Herglotz's trick to show the real case and analytic continuation for the complex case.

License

BSD License

Topics

Session Cotangent_PFD_Formula