  If we cannot obtain all terms of a series, or if we cannot sum up a series,
we have to turn to the partial sum approximation which approximate a function
by the first several terms of the series. However, the partial sum
approximation often does not work well for periodic functions. In the partial
sum approximation of a periodic function, there exists an incorrect oscillation
which cannot be eliminated by keeping more terms, especially at the domain
endpoints. A famous example is the Gibbs phenomenon in the Fourier expansion.
In the paper, we suggest an approach for eliminating such oscillations in the
partial sum approximation of periodic functions.
