= Solution
The required property is \b[odd symmetry], $\boxed{f(-x)=-f(x)}$, up to irrelevant changes on a set of measure zero when discussing <Fourier coefficients>. An <odd function> has zero mean, and its products with <cosine> are odd, so every <cosine> coefficient vanishes. Its <sine> coefficients may remain nonzero.
For pointwise representation, the <Fourier series> takes the average of the one-sided limits at a jump. In particular a pure <Fourier sine series> has value zero at the origin and at the endpoints; arbitrary assigned values there need not equal the series sum.
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