Reference on a paper by Riemann on Fourier

Question

I was watching a video on PDEs and when arriving at the part of Fourier Series, the professor said:

And one of the most fascinating reads I ever had was a paper by Riemann on the history of this [Fourier Series].

I tried looking for it but didn't succeed, and I was wondering if anyone could provide a link or a reference to this paper.

Thank you very much.

In case you need it, the link of the video is: https://www.youtube.com/watch?v=cf8rgx60IKA on the minute 14:21 (The audio on that specific part is messed up, so be careful if you are using headphones).

Answer 1

Riemann only wrote one paper on Fourier series: his Habilitation thesis "Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe" (On the representability of a function by a trigonometric series). This is where he famously what it means for a function to be integrable in the manner named after him, and less famously, integrates by parts a couple of times.

A transcription is available here. Translations are hard to come by (see here for some references). There is a French edition of Riemann's Oeuvres available here if French is more comprehensible than German, but otherwise you'll probably have to hunt down the Kendrick Press translation by Baker, Christenson and Orde.

Answer 2

That's Riemann's Habilitationsschrift: "Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe". (1853-1854)

Reference might be formatted like this:

G.F.B. Riemann, Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe. In: Bernhard Riemann, Gesammelte mathematische Werke, Leipzig, Teubner, 1892, pp.227-264

PDF link: http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Trig/Trig.pdf

Google books: G F B Riemann, Gesammelte mathematische Werke, pp.227-264 https://books.google.com/books?id=fSzfCXZrvOwC