Are all the non-elementary functions that is not piecewise expressible as an infinite series of elementary functions?
details about elementary function - http://en.wikipedia.org/wiki/Elementary_function
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Every analytic function is is locally expressable as a power series. Every periodic function can be expressed as a Fourier series (except at discontinuities, where they might disagree). – Apr 05 '14 at 18:05
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If you're willing to take 'locally a power series' then the answer is yes by Fourier series. – Apr 05 '14 at 18:09