Question: Hi Alex, If you know what a Fourier series is, then a very easy proof would be accessible to you  you can find it in any text that introduces Fourier series. It also follows from other advanced concepts, so it can be found in many books on analysis or complex analysis.
Elementary proofs appear frequently in math journals.
68 (1961) 485487 80:4 (1973) 424425 and also 425431 85:6 (1978) 481483 94:7 (1987) 662663 Also, there is a proof in MATHEMATICS MAGAZINE 45:3 (1972) 148149. Most of these articles list further examples in their references. If you would like us to send you a copy of one of these articles, please let us know. Chris
