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\title{Fourier Series}
\author{Lawrence C Paulson}
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\begin{abstract}
This development formalises the square integrable functions over the reals and the basics of Fourier series. It culminates with a proof that every well-behaved periodic function can be approximated by a Fourier series. The material is ported from HOL Light.\footnote{\url{https://github.com/jrh13/hol-light/blob/master/100/fourier.ml}}
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\section{Acknowledgements}
The author was supported by the ERC Advanced Grant ALEXANDRIA (Project 742178) funded by the European Research Council.

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